Beam dynamics design rules

Protons: T (Mev) = 3.12 x 10-4 B2R2 ... the radius R applies to the extent of the uniform magnetic field; the physical radius of pole faces must be larger by about one-half the gap length.

Livingston & Blewett, Particle Accelerators (1962) — p. 158

Tabletop: For 8-in poles at 5.9 kG with ~1.5-in gap, usable R is roughly 3.25 in, predicting ~115 keV; a wider pole or smaller gap directly buys energy as B^2R^2.

for particle oscillations about an equilibrium orbit to be stable for both axial and radial coordinates, the value of n must be in the range 0 < n < 1.

Livingston & Blewett, Particle Accelerators (1962) — p. 161

Tabletop: Map n(r) on the 8-in poles; any region where field rises with radius (n<0) defocuses axially and kills the beam.

the total decrease below the value of the central field out to the exit slit is about 2 per cent. The radial decrease can be larger (3 to 4 per cent) in small machines in which D voltage is relatively high.

Livingston & Blewett, Particle Accelerators (1962) — p. 161

Tabletop: The reference machine is the 'small, few-turn' case: aim for a smooth 3-4% droop center-to-edge rather than a flat field.

The n value rises almost linearly from zero at the center to 0.02 at 15 in. (where fringing effects start), then increases rapidly to 0.40 at 18.75 in. (exit-slit location) and to 1.0 at 19.25 in.

Livingston & Blewett, Particle Accelerators (1962) — p. 161-183

Tabletop: Scale directly: on 8-in poles keep n tiny out to ~3 in radius and take the beam off where n has climbed to ~0.4.

the magnet generates 2.7 T of magnetic field with a 1.25 inch pole separation... capable of accelerating protons to a maximum kinetic energy of 1.96 MeV

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 7-8

Tabletop: The surplus-NMR-magnet route to MeV energies: small radius is fully compensated by high B (energy ~ B^2*r^2), so a 6-inch 2.7 T machine beats a 12-inch 1 T machine.

implement a .02'' convex taper from the center of the pole to the edge, to create sufficient bending of the magnetic field lines.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31

Tabletop: A concrete starting number for 8-12 inch poles; the same 0.02 in figure was used on 12 inch poles at 1.6 T, so it scales directly to a next machine.

at a dee radius of 6'' the field is 1.57 T, a .08 T drop off from 1.64 T directly at the center.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31

Tabletop: Gives the builder a sanity band for their own field maps: a few percent droop is by design, much more costs resonance synchronism.

To minimize weight and size of magnet system the average magnetic field value has to be high, limited by iron saturation ... average magnetic field value was chosen as 1.4 T provided of 2.3 T and 0.5 T of hill and valley region fields

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 1

Tabletop: The hill/valley ratio (~4.6:1) and 45-degree sector angle are directly scalable to an 8-12 inch AVF pole set; iron saturation, not coil power, is the ceiling.

As hill gap providing enough beam intensity was chosen as 20 mm and then corresponding valley gap is 100 mm.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 1

Tabletop: Gives the gap ratio for a first AVF pole-tip design; a deep valley is also where an amateur puts the Dee/RF and pumping.

The reason for increased radial oscillations is big first harmonic of magnetic field, which caused by non-symmetric structure of central part of cyclotron magnet ... to make symmetric central magnet part by setup second hole on opposite side with respect to ion source hole.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 2-3

Tabletop: A ten-fold reduction in orbit wander for the cost of drilling a second, unused hole - directly applicable to any asymmetric feature in the reference machine's pole or chamber center.

the fringe field is longer at the center of the magnet and drops off near the edges. This distribution is approximately quadratic and the integrated multipole field looks like a sextupole field.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 20-21

Tabletop: Mostly relevant if the builder adds edge shaping for extraction: expect the field falloff at the pole rim to vary azimuthally with any non-axisymmetric pole feature, and fix it empirically with removable machined inserts.

Shimming of pole edges or shims based on equation: dB(r)/B(r) = gamma(r)^2 * df_p(r)/f_p(r)

Zaremba, Magnets for Cyclotrons (2005) — p. 10

Tabletop: At 160 keV-1 MeV gamma ~ 1.0002-1.001, so isochronism errors are dominated by mechanical field errors, not relativity - this formula converts the reference machine's measured phase-slip vs radius directly into required shim thickness profile.

The maximum kinetic energy T determines magnetic rigidity: B*rho = sqrt(T^2+2T*E0)/(300*Z)

Zaremba, Magnets for Cyclotrons (2005) — p. 19

Tabletop: For 1 MeV protons B*rho = 0.145 T*m: at 1 T that is a 14.5 cm final orbit radius, which immediately sizes the next machine's pole diameter (with overhang and fringe allowances added).

coil cooling estimation: dT(C) = 60*P(kW)/(4.19*N(l/min))

Zaremba, Magnets for Cyclotrons (2005) — p. 30-32

Tabletop: The cooling formula is immediately usable: a next machine's 5 kW coil at 4 L/min runs ~18 C water rise; the flutter formulas matter only if the builder adds sector (AVF) pole faces.

For best RF efficiency, k=0.5 BUT to decrease machine dimensions k >0.5 (more hill, thus more field) CHOICE : k=0.67 (60 deg hills)... CHOICE : nu_z = 0.2

Zaremba, Magnets for Cyclotrons (2005) — p. 32-33

Tabletop: If a next machine goes AVF to escape the weak-focusing energy ceiling, these are proven starting numbers: 3 or 4 sectors, half-open valleys, and a modest nu_z ~ 0.2 target.

A general rule of thumb is that the length of the fringe field beyond the edge of the steel pole tip is = h, = h/2, or = h/3, for the dipole, quadrupole or sextupole

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 252-253

Tabletop: Tells the builder where their usable field really stops on an 8 inch pole: with a ~2 inch gap the field is already dying ~1 inch inside the pole edge, which sets the practical maximum orbit radius and extraction geometry.

the radial sector poletips have the greatest average falloff - so great that it amounts to be an unusable field. The spiral sector AVF field is a compromise between the two.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 10

Tabletop: Direct guidance for a next machine's pole-tip upgrade at the 8-12 inch scale; also warns that narrow spiral vanes saturate at large radius (measured field fell below simulation).

this analysis approach can be used to quickly assess a field during design, relegating the laborious task of phase space mapping and determining the limits of stability to the few the final contenders.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 10-11

Tabletop: A cheap, quantitative design filter that works from measured maps of a home-built magnet, no orbit code required.

we choose a reference circle to have a radius half that of the maximum ion radius ... the reference circle is swept to maximize the 4th harmonic, while minimizing the second, third, and fifth.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 6-7

Tabletop: Applies if a next machine moves to sectored pole tips; on a 12-inch machine the whole analysis is a spreadsheet/Octave job on the map you already took.

The vertical field magnitude decreases away from the magnet over a scale length comparable to the gap width.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 140, 526

Tabletop: Rule of thumb for a next machine's layout: reserve roughly one gap-height of radius at the pole edge as unusable fringe, and shield any deflector with a grounded septum.

fx = (gamma mo vz/qBo)/tan beta = rgo/tan beta.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 141

Tabletop: If a next machine ever extracts a beam, angling the magnet exit edge focuses the diverging beam without any extra magnet.

The bending magnets were shaped to produce a field with index in the range 0 < n < 1.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 159, 521

Tabletop: The outer bound that pairs with Koeth's n<0.2 refinement: the reference machine's field must fall (n>0), but slowly, all the way to full radius.

Tmax = 48 (Z RB)2/A, where Tmax is given in MeV, R in meters, and B in tesla.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 524

Tabletop: The master sizing formula: the reference machine's 0.59 T at ~0.09 m gives ~135 keV; 1 MeV needs (R*B) ~ 0.144 T-m, e.g. 1.2 T at 12 cm.

Have real sinusoidal solutions for 0<n<1; this condition is true in a classical cyclotron

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 36-37

Tabletop: Confirms the reference machine's flat-pole H-frame inherently provides weak focusing from its natural radial falloff - the design task is controlling how fast n rises, not creating it.

Almost (but not quite) spherical: Efficient cyclotron magnetic circuits include more iron laterally than axially

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 48-50

Tabletop: The B^2 energy leverage argues for pushing the next machine's field toward the iron limit (~1.5-1.8 T) before enlarging poles: doubling B quadruples energy at fixed radius while iron mass stays fixed.

A radially decreasing field can be described as Bz = B0(r0/r)^n for n >= 0, where n = 0 implies a uniform field and n > 0 implies a restoring force.

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 7-9

Tabletop: Exactly the reference machine's problem class and size: machine a gentle crown or stepped 'lump' into the 8-inch poles (or shim equivalently) targeting ~2-3% center-to-edge fall-off for axial focusing.

For educational applications a six to nine-inch pole piece is an economical range; for inducing light element reactions ... a somewhat larger machine, say, 12 to 15 inches

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 11-12

Tabletop: Directly frames the next machine's decision: staying at 8 inches keeps it a demonstration machine; nuclear-reaction goals argue for 12-inch-class poles and higher field.

Slight taper on pole applies a corrective Lorenz force to the beam. Made with freeware! Poisson Superfish

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 8

Tabletop: Confirms the standard amateur approach for the reference machine's scale: put the field index into the pole profile (taper/gap growth with radius) rather than relying on accidental fringing.

the field index value n=0.2 must not occur inside the maximum ion orbit radius to avoid coupled resonances

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 2, 39

Tabletop: This is the single design criterion for weak-focusing pole shaping on a 100 keV-1 MeV tabletop machine; it is computable from a measured B(r) curve.

weak magnetic focusing can be achieved by producing a magnetic field in which Bz linearly decreases.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 26-27

Tabletop: Gives a single, plottable acceptance test for a shimming attempt on the reference machine's 8-inch poles - no orbit code needed to reject a bad shim.

the magnetic field actually increases in magnitude out to around r = 5 cm at which point it begins decreasing again. This is problematic because it yields a negative field index

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 51-53

Tabletop: A concrete trap when adding any iron or coil near the center of an 8-inch pole; check the sign of dB/dr everywhere, not just at the edge.

the difference in radius is minimal - about 0.2 cm - and comes at the steep cost of a ~20% reduction in maximum magnetic field from 1.27 T to 1.07 T. As such, this modification was considered insufficient.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 53-54

Tabletop: Saves a next machine's builder from spending months on trim coils inside a small gap; also note trim coils steal gap height.

Pole face: 150mm, Pole gap: 39mm, Current: 70A ;NOTE: this is a slice down the middle of the magnet

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 60-68

Tabletop: Zero-cost simulation path for a hobbyist; the appendix geometry file is a working starting template for an 8-15 cm pole magnet.

much of the beam current is being lost by the time the beam reaches larger radii... This could be done by adding shims of ferromagnetic material between the chamber and pole faces.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 52-53

Tabletop: Predicts the current-vs-radius profile the builder should measure, and the standard shim fix if a next machine loses beam before full radius.

the value of n for the cyclotron must be between 0 and 1; it has been determined empirically the index should increase with r roughly linearly between 0 and 1

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 21-23

Tabletop: The core magnet-shimming target for the next machine: map B(r) with a Hall probe, compute n(r) by finite differences, and add edge shims until n(r) is a clean 0-to-1 ramp over the dee radius.

The magnet's upper and lower coils are independently energized enabling an intentional axial field imbalance so as to vertically shift the accelerating plane.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 2

Tabletop: Cheap beam-height trim for a next machine: two supplies (or a shunt rheostat on one coil) instead of re-machining anything.

if n = 0.2 is to be avoided (vx=2vz), then the rate at which the vertical field decreases must be moderated such that n=0.2 occurs at the final ion radius.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 3

Tabletop: The quantitative pole-taper design rule for a next machine: map n(r) from the field profile and keep 0 < n < 0.2 out to full beam radius.

The n=0.2 location occurs near r=3.5 inches, well within the 5 inch DEE radius, so as to allow the ion displacement to grow.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 5

Tabletop: Shows how little margin there is between good and bad tapers on an 8-12 inch machine; motivates measuring n(r), not guessing it.

The axial tune... can be summarized by: vz2 = -k + F(1+tan2xi) and the radial tune is written as: vr2 = 1+k

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 6

Tabletop: If a next machine ever gets sector pole tips (to allow a rising average field), these two lines are the whole first-order design calculation.

F = ((<B^2> - <B>^2)/<B>^2) is called the flutter and represents the hill to valley field difference

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 25-26

Tabletop: The complete design equation set for an AVF follow-on build; every term is measurable from a 2-D Hall-probe map of the built magnet.

N large: high maximum energy, F small and quasi circular orbits -> spiral compulsory

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 26, 28

Tabletop: Explains when the extra machining pain of spiral tips pays off; at 8-12 inch pole size with N=4 a modest spiral is worth more than more sectors.

It implies that N must be larger than 2 (lower limit of the pi stop-band) and there is an energy limit for every N value T = (N/2 - 1)E0

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 27-28

Tabletop: Rules out 2-sector 'butterfly' pole tips that look easy to machine; N=3 or 4 is the practical amateur choice and neither limits sub-MeV protons.

For best RF efficiency, k=0.5 BUT to decrease machine dimensions k >0.5 (more hill, thus more field) CHOICE : k=0.67 (60 deg hills)

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 69

Tabletop: Shows the exact arithmetic used to go from a required <B> to hill/valley fields and sector angle - reusable at any scale.

CHOICE : nu_z = 0.2. Flutter and spiral not too large. Field gradient can be strong. Spiral angle of pole completely determined since n, N, F and nu_z are known

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 69

Tabletop: Gives a numeric focusing target to design toward instead of 'as much focusing as possible' - and 0.2 is achievable with weak focusing at the reference machine's energies.

The radial decrease in field strength is at a rate of one percent in 13 inches out to a radius of 20 inches ... These shims reduce azimuthal variations to less than 0.2%.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 15, 35

Tabletop: The fractional numbers transfer, not the inches: aim for a smooth ~1-3% total field fall-off center-to-edge on the 8-inch pole and shim azimuthal asymmetry to the few-per-mille level.

By means of auxiliary coils wound on the pole pieces it is possible to control the position of the beam with respect to the median plane of the tank.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35

Tabletop: Directly applicable and cheap for a next machine: a few dozen turns on one pole with a bipolar bench supply gives a knob for vertical beam centering instead of mechanical re-shimming.

Increasing the dee voltage, however, requires increasing the required voltage breakdown gap and thus the magnet hill gap, so that some compromise must be reached.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 65

Tabletop: The coupled optimization transfers: for a next machine, pick dee voltage and magnet gap together, since every kV of dee needs clearance that costs ampere-turns.

the design of the beam deflection system will be worked out simultaneously with the design of the magnet ... all the problems which arise from trying to obtain deflected beams after the machine is built would be avoided.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 85-86

Tabletop: Directly applicable lesson for a next machine: if an extracted beam is ever wanted, reserve the azimuthal slot, field-edge profile, and feedthrough ports now, even if the deflector comes later.

an input RF power level of 50 watts is too low, and 500 watts should be sufficient. The first ions are expected to clear the chimney at approximately 200 watts.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 5

Tabletop: A geometry trap for a next machine: any chimney or source structure must be smaller than the first half-turn diameter set by the dee voltage, or beam dies before the first gap crossing.

Protons: f (megacycles) = 1.52B (kilogauss) ... The actual technique used to control resonance in a cyclotron is to vary the magnetic field, with the applied frequency held constant.

Livingston & Blewett, Particle Accelerators (1962) — p. 156

Tabletop: The reference machine's 0.59 T (5.9 kG) gives 8.97 MHz, confirming their ~9 MHz choice; for a next machine pick B first, then f = 1.52*B.

there will be a somewhat lower potential at the ends of the D faces nearest the lines ... measured in some cyclotrons to be as great as 5 per cent ... a displacement of the ion source of over 2 in. has been necessary.

Livingston & Blewett, Particle Accelerators (1962) — p. 164

Tabletop: Make the source mount adjustable by a few mm in both directions and tune position for beam, not for geometric center.

the practical maximum migration in phase will be from zero to -pi/2 and back to zero, a total phase migration of pi radians or one half-cycle.

Livingston & Blewett, Particle Accelerators (1962) — p. 166-171

Tabletop: With a 3-4% field droop and 160 turns-scale acceleration, the reference machine's dee voltage sets how much phase slip they can afford: higher V = fewer turns = more field-shape tolerance.

Increasing the D voltage requires fewer turns for acceleration to maximum energy and will compensate for a larger phase shift. However, D voltage is usually limited by ... power and spark breakdown.

Livingston & Blewett, Particle Accelerators (1962) — p. 172

Tabletop: At 1.3 kV and 160 keV the reference machine's ions make ~60+ turns; doubling dee voltage halves turns and dramatically relaxes both field-uniformity and vacuum (scattering) requirements.

apply a radio frequency oscillating voltage to the electrode that is slightly less than the cyclotron frequency given at the center of the field, but greater than [that] near the edges.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 20

Tabletop: A concrete tuning rule for the builder: don't tune RF to the central field value; split the difference toward the outer-radius field.

It would only take a few cycles, on the order of 12, for most cyclotrons to have reached this velocity.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 20

Tabletop: Quantifies how little phase budget a mistuned tabletop machine has; explains failed runs where beam dies at small radius.

This value is about 10% for 120 uamp of deflected deuterons, increasing to 15% for a 200 uamp beam. About 30% of the internal beam at the exit radius is extracted.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 19

Tabletop: Sets expectations if a next machine attempts a deflector: losing two-thirds of the beam at the septum is normal, not failure.

fo = qBo/2pi mi = (1.52x10^7) Bo(tesla)/A

Humphries, Principles of Charged Particle Acceleration (1986) — p. 524

Tabletop: One-line check of the reference machine's operating point: 0.59 T -> ~9.0 MHz for protons; sets the next machine's RF band for any target field.

the final kinetic energy is maximized by taking Vo large... a high gap voltage accelerates particles in fewer revolutions so that there is less opportunity... to get out of synchronization.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 530-531

Tabletop: At sub-MeV this limit is distant (10 kV dee -> ~3 MeV proton ceiling), but the same physics governs field-flatness tolerance: fewer turns forgives more field error.

Low energy proton in 1 T field: 15.23 MHz

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 29

Tabletop: The single most-used number in the reference machine's notebook: 0.59 T -> 9.0 MHz; a 1.2 T higher-field successor -> 18.3 MHz, still comfortable amateur-radio-technique territory.

250 MeV protons; 17 KeV/turn: N~15,000... 250 MeV protons r=0.3m: dr/dN ~ 20 microns!

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 43

Tabletop: For the builder: 1 MeV at 2 kV/gap (2 gaps) is ~250 turns with final-orbit spacing ~0.2 mm at r=12 cm - explaining why higher dee voltage directly eases both extraction and vacuum requirements.

dphi/dn=360 [gamma-1] -> 8 deg. An ion on peak phase is lost in 11 revolutions. Only solution- very high energy gain per turn - 360kV

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 51

Tabletop: Reassurance and ceiling in one number: at 1 MeV gamma-1 = 0.001, ~0.4 deg/turn - a next machine is nowhere near the relativistic limit, and the classical (non-AVF) architecture is fine to several MeV.

the 'single-dee' construction; this has many advantages ... Better ion focussing can be obtained by installing a 'dummy' grounded dee edge symmetric to the insulated dee, but this is a refinement

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8

Tabletop: Exactly the reference machine's architecture; the dummy-dee edge is a proven low-cost next-machine upgrade for a cleaner accelerating gap.

No peaks for magnetic fields larger than H2+ at 0.5 T -> 35 keV; 44 orbits at 800 Vpp

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 21

Tabletop: Quantifies why the reference machine's dee-voltage upgrade matters: at 1.3 kV their protons need ~hundreds of turns to reach interesting energies, and ~44 turns was already the survival ceiling at Houghton's pressures.

The axial component of the magnetic field can be decreased at larger radii in order to increase the radial (focusing) component, provided the ions only have a few revolutions left once they reach this portion of the field.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 27-28

Tabletop: Explains why the reference machine's next big win may be Dee voltage, not magnet shaping: at ~160 keV with a low Dee voltage the turn count is what kills the beam.

It can be seen that in general, an increase in dee voltage results in a higher beam current.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 49-50

Tabletop: For a fill-gas machine like the reference machine's, dee volts are the strongest single knob on beam current; prioritize RF voltage over almost everything else.

higher potential on the dees results in fewer orbits and a shorter time of acceleration, allowing for a higher maximum kinetic energy... gives a maximum of 15 MeV for protons with 50 kV peak-to-peak

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 24-26

Tabletop: At the reference machine's sub-MeV energies relativistic slip is negligible (~0.1%), so dee voltage matters mainly through path length and gas scattering - but this rule sets the fixed-frequency ceiling for any future MeV-class ambition.

It is possible to calculate the various effects quantitatively and to predict the minimum dee voltage required to obtain a given energy in a particular cyclotron.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 17-19

Tabletop: Directly applicable design step for a next machine: compute threshold voltage for the target energy and field taper before freezing the RF chain power budget.

As measured, efficiency tends to increase with dee-to-dee potential and with beam power.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 24-26

Tabletop: Order-of-magnitude expectation transfers: most RF power goes to resonator and ion-loading losses, so judge a next machine's RF sizing on resonator dissipation, not beam power.

the maximum voltage gain/dee is Vd = 2*V0 sin(theta/2); for particles rotating on subharmonics of the dee frequency the angular width of the dee is n*theta to the particle

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 100

Tabletop: Directly applicable when the builder trims a next machine's dee for probe or source clearance: keep the dee close to 180 degrees or account for the sin(theta/2) energy-gain penalty.

the beam width was found to be limited by the internal aperture of the D's out to about one-third of the final radius and then to narrow in a nearly linear fashion out to the exit slit.

Livingston & Blewett, Particle Accelerators (1962) — p. 163-167

Tabletop: Give the first third of radius generous vertical aperture (that is where ions are lost); the outer region can be tight, which also helps RF economy.

There is no vertical magnetic focusing at the center of the magnet. By a fortunate coincidence, electrostatic focusing by the accelerating fields is effective for low-energy ions.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 524, 526

Tabletop: Explains why source-to-dee geometry (chimney position, puller gap, aperture height) dominates beam capture on small machines: the magnet cannot help until several turns out.

some 90% of the initial supply of ions are lost to the dee surfaces. The loss may be reduced by increasing the dee voltage, thus reducing the number of turns an ion makes

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 18

Tabletop: Directly applicable: at 1.3 kV the reference machine's protons make many turns; the single biggest transmission lever for a next machine is more dee volts, not more source current.

In more practical units, this equation can be rewritten: j[mA/cm2] = 1.72 * sqrt(q*/u) * phi[kV]^(3/2) / d[mm]^2.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 376-377

Tabletop: Confirms the reference machine's nA beams are nowhere near space-charge limits; if extraction is weak the problem is geometry/plasma matching, not the Child-Langmuir ceiling.

The assumption of a certain aspect ratio (aperture radius to electrode separation). A good aspect ratio is on the order of S = 0.5.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 379

Tabletop: For the puller gap in a next machine: make the source-slit half-width about half the slit-to-puller distance, then tune arc density (not geometry) until the beam is parallel.

at a pressure of 0.4 mTorr and 10.5 W PIG source power, a continuous 1 mA positive hydrogen ion beam has been focused onto the target and accelerator voltages up to -30 kV have been investigated.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 3

Tabletop: Template for a bench extraction test stand to characterize the next machine's source before it goes into the magnet.

The chimney with the larger slit produces a beam with a larger emittance. However, the beam is also of higher intensity.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 66-69

Tabletop: Tells the builder exactly what to expect when they widen their next machine's chimney slit: current scales faster than linearly with width, emittance grows more slowly - widen until the machine acceptance is filled.

an approximately flat plasma boundary provides the best match to the experimental beams emerging from the 'slit' style chimneys... while a concave plasma boundary... for the 'hole' style chimney

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 73-76, 91-107

Tabletop: Decides a next machine's chimney aperture style: cut a tall narrow slit, not a drilled hole, if beam brightness and predictable optics matter.

the general trend of increasing arc current producing increased beam current as expected... there was no noticeable change in the emittance of the beam for different currents

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 77-78, 81

Tabletop: For the builder: cranking arc power buys current with diminishing returns but does not spoil beam quality below ~230 uA - space charge is negligible at their nA-uA scale.

the plasma temperature that provides the best match for experimental beams is approximately 35,000 K (resulting in a central starting energy of 4.5 eV).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 91-107

Tabletop: Gives the builder the initial-condition recipe for any first-turn orbit simulation of their next machine's central region.

An acceptable vacuum would allow for a mean free path an order of magnitude larger than the expected flight distance.

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 9-11

Tabletop: The quantitative vacuum spec for a next machine: total path length ~ (final energy)/(energy per turn) x orbit circumference; halving dee voltage doubles path length and tightens the pressure requirement proportionally.

A typical figure, used in the MIT cyclotron, is a dR of 0.15R. The deflector gap is usually tapered ... Spacings as small as 1/8 in. can be used at the entry slit, opening to 1/2 in. or greater at the exit.

Livingston & Blewett, Particle Accelerators (1962) — p. 180-181

Tabletop: Scaled to 160 keV the same geometry needs only ~500-900 V on the deflector - an easy supply; keep the entry slit no wider than the turn separation.

It is seen that particles are detected at about 70 kv. and the numbers increase more rapidly with increase of bombarding energy than with the lithium film.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 266-270

Tabletop: Proof that p-B11 alphas are observable far below the 675 keV resonance if the builder integrates tens of uA-hours with large solid angle - and that their alphas stop in under 5 cm of air (vacuum path to PIPS required).

the ion revolution turn spacing near r = 4 inches, in a B-field of 1.0T will be just 0.04 inches, which is smaller than the 0.06 inch RF shield of the tip

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 1

Tabletop: At the reference machine's ~1.3 kV dee voltage turn spacing is even smaller, so a bare, grooved copper collector (no thick shield) is essential or the probe reads zero while beam exists.

The limit at the entry is set by the dr between successive turns at this radius ... it is desirable to have adjustable controls on deflector spacing and location which can be trimmed empirically.

Livingston & Blewett, Particle Accelerators (1962) — p. 181-183

Tabletop: With 2.6 kV/turn on 160 keV, the reference machine's turn spacing at extraction is ~1.6% of R (~1.3 mm at 3.2 in) - build the septum mount with mm-scale radial adjustment.

Emergent beam intensities up to 25 per cent of the resonant beam intensity have been obtained under optimum conditions ... practical operating intensities would in this case be limited to 80 or 100 ua.

Livingston & Blewett, Particle Accelerators (1962) — p. 182

Tabletop: Judge a next machine first on internal-probe current at full radius; a 4:1 ratio between internal and extracted beam is historically normal, not a failure.

the septum is formed of two strips of tungsten, 0.020 in. thick and 12 in. long and with the edges spaced 1/8 in. apart. Each strip is silver-soldered to a copper bar bent to the correct curvature.

Livingston & Blewett, Particle Accelerators (1962) — p. 184

Tabletop: At the reference machine's microamp/keV beam power the thermal problem vanishes, but the slotted-septum geometry still maximizes transmitted current into the channel.

once the particle has been accelerated to 10 MeV the mass has been changed by about 1%, which has a frequency shift of 1%.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 12, 21

Tabletop: Reassurance with numbers: at the reference machine's 100 keV-1 MeV scale, relativistic detuning is ~0.01-0.1% and can be ignored in a next machine's design.

The separation for non-relativistic ions is dR = (R/2) (2qVo sin phi_s/T)... Eq. (15.3) implies that dR = 0.44 cm.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 527

Tabletop: Lets the builder compute whether their probe or a future septum can distinguish final turns: at 150 keV, R~9 cm and 5 kV/turn gives dR ~ 3 mm - workable.

0.15 0.91 +/- 0.015... 0.65 218.42 +/- 0.55

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 360

Tabletop: The master rate table for the reference machine's PIPS count-rate prediction across their entire 150-675 keV window; it quantifies exactly what reaching the resonance is worth.

Vd = 32.531 kV

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 6

Tabletop: Gives the builder the extraction-voltage scale for a next machine: deflector kV requirements scale linearly with beam energy, so a ~100 keV beam needs only ~7 kV in the same geometry.

H2+/9 H+/7 H+/5 H+/3 H+ H2+

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 15-18

Tabletop: Prevents misidentifying beam in the reference machine's B-field sweeps: a peak at one-third the expected field is the same ion on the 3rd harmonic, not a new species.

At -25 kV, 8 mA, and 16 mtorr, neutron levels were 60 cpm. This measurement confirmed that nuclear fusion was achieved.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 45-46

Tabletop: Same lesson as p-B11 cross-section curves: yield is exponential-ish in particle energy, so for the builder every extra 10% beam energy buys far more counts than 10% more current.

It was limited to low level output by its 22kv internal supply. 103 n/sec... a 33 kilovolt supply. 105 n/sec... currently produces in excess of 600,000 neutrons per second

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 36-39

Tabletop: Reinforces the energy-over-current rule for the builder: sub-Coulomb-barrier reaction rates reward every extra keV exponentially.

If many ions in the beam fall out of phase before reaching maximum Dee radius, the beam current will drop suddenly to near zero beyond whatever radius the ions tend to reach

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 28, 57

Tabletop: Diagnostic rule: a sharp cutoff in the radial current profile means phase slip, not wall collisions - which points at field shape/Dee voltage rather than focusing.

for a fixed frequency f, resonances will occur for lower magnetic fields, e.g. B/3 and B/5, corresponding to an odd multiple of a lower frequency

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 4-5

Tabletop: Practical commissioning technique: the builder can confirm they are accelerating protons (not H2+ or contaminants) with only a magnet current sweep and an electrometer.

Frame-by-frame analysis... revealed that ions nominally populate 40 degrees of the 360 degree RF cycle in our cyclotron.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 9

Tabletop: Sets expectations for pulsed diagnostics and duty-factor arithmetic on any measurement the builder makes with fast instrumentation.

The axial focusing, as shown above, takes place for any positive values of the field decay exponent. Therefore, orbital stability in both directions takes place only for 0 < n < 1.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 18-20

Tabletop: This is the governing stability rule for the weak-focusing reference machine; the FEMM-derived B(r) should be checked for 0 < n < 1 over every acceleration radius, with n typically a few percent.

its passage without noticeable losses of particles becomes possible only due to the fact that the beam crosses it for 1-3 revolutions, and the first harmonic of the magnetic field with a large amplitude is absent

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 37

Tabletop: In the reference machine Qr = sqrt(1-n) sits just below 1 everywhere, so the key is field symmetry: keep the first-harmonic error (pole tilt, off-center coils) to gauss level or coherent orbit distortion grows every turn.

When transferring the energy of radial betatron oscillations into axial oscillations, the amplitude of the latter turns out to be twice the amplitude of radial oscillations.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 39

Tabletop: Very concrete for the reference machine: if the edge-field falloff pushes n through 0.2 near the last turns, the beam blows up vertically into the dee aperture; keep n < ~0.2 until the extraction radius or cross it fast.

if the field is formed such that the deviation from the isochronous one for all operating radii is no more than 5 G, then this corresponds to a deviation of the RF phase... by no more than 5 degrees

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50

Tabletop: A concrete shimming target: on a 0.59 T, 8-inch machine, holding the measured field to ~1e-3 of the design curve (a few gauss) keeps phase errors negligible next to the classical-cyclotron phase slip itself.

the level of the magnetic field in the center is raised to an amount of a few tens to a few hundred gauss

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50-51

Tabletop: Directly usable on a next machine: shim a small central cone so B falls gently from center outward, giving vertical focusing where n ~ 0 would otherwise leave the first turns unfocused.

The presence of the resonance makes it possible to use the first harmonic of the field with a small amplitude (usually a few gauss) to obtain a significant increase in radial amplitudes.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 64-65

Tabletop: The dR formula tells the builder exactly what turn spacing a ~kV energy gain buys at 4-inch radius (fractions of a mm), i.e. whether a septum/foil extraction is geometrically feasible for a next machine.

By selecting the value of the generator frequency, it is possible to achieve that the point of changing the direction of the phase motion is near -90 degrees.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 22

Tabletop: Directly applicable: at 100 keV-1 MeV the reference machine is far from the ceiling, but deliberately detuning the oscillator slightly low buys extra phase headroom against an imperfect field profile.

the optimal case from the viewpoint of minimizing the radial beam losses is a mode of operation in which the value of the injection energy is less than the amplitude of the accelerating voltage across the dees

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 55-56

Tabletop: If a next machine ever moves to an external source and axial injection, inject at a few kV below the dee amplitude rather than pushing injection energy up for easier transport.

the phase acceptance of the center, as a rule, contains the particles, the initial RF phases of which do not go beyond the range of (-90; 20)

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 56

Tabletop: Explains why only ~30% of source output ever accelerates in the reference machine; the builder tool should launch macroparticles over this window rather than a single reference phase.

The number of lost particles dN at each time step dt can be estimated by the formula dN = sigma nN v dt

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 70

Tabletop: Lets the builder tool convert the reference machine's gauge reading and total path length (hundreds of turns) into a survival fraction, quantifying how much beam a ~1e-5 Torr vacuum costs versus 1e-6.

The slit is most functional if it is installed in the place of the largest radial size of the beam... The closer to the center the device is installed, the more efficient it is

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 56

Tabletop: Practical placement rules if the builder adds a beam-defining post or slit to clean up phase spread and improve turn separation at extraction radius.

Most often, the boundary of the transition to high intensities is determined at the level of a few hundred microamperes.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 40

Tabletop: The reference machine's nA-uA internal beams are 2-4 orders below the threshold: the builder tool can safely omit space-charge solvers entirely, a major simplification.

the relative radial increase is only half the relative energy increase. However, for a given cyclotron, the turn separation dr0 will double when the dee voltage is doubled.

Kleeven & Zaremba, Cyclotrons: Magnetic Design and Beam Dynamics — CAS 2015, arXiv:1804.08961 (2018) — p. 44

Tabletop: The reference machine (155 keV, 2.6 keV/turn, r=9.65 cm) gets only ~0.8 mm/turn; a 10 kV dee at the same radius gives ~3-6 mm.

for a final energy of T = 30 MeV, dT = 100 keV, and an extraction radius of 0.5 m, we find dr = 0.83 mm. This is a rather small number, e.g. when compared with a radial beam width of for instance 4 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 6

Tabletop: Small machines fare better because dr scales as dE/E; a 350 keV next machine at 10-20 keV/turn beats this 30 MeV machine's fractional separation by ~50x.

when a coherent oscillation amplitude x of 3 mm has been built up ... and acceleration takes place until vr = 0.8, the maximum turn separation due to precession is 3.8 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 7

Tabletop: A deliberate few-mm source off-centering plus letting the beam run into the fringe (n rising to 0.2-0.4) can triple the next machine's turn spacing for free.

In practice, a coherent radial oscillation amplitude of the same size as the incoherent amplitude, is a good criterion for efficient extraction.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 7

Tabletop: If a next machine's radial beam half-width is ~2-3 mm, aim for a ~2-3 mm coherent amplitude, no more.

one has to limit the radial amplitude, induced from the v = 1 resonance, to a few mm.

Heikkinen, Injection and Extraction for Cyclotrons — CAS, CERN 94-01 (1994) — p. 18

Tabletop: In a weak-focusing field the last turns sweep n from ~0.1 to ~0.5; keep energy gain high there so n=0.2 is crossed in <~5 turns.

taking eps1 = 10-4, R = 1 m and vr - 1 = 0.01, one finds an orbit centre shift, i.e. a radial oscillation amplitude, of dx = 5 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 9

Tabletop: Gauss-level azimuthal field asymmetry matters at 0.59-0.89 T: it is both the knob (deliberate shim/coil bump) and the hazard (uncontrolled bumps de-center the beam).

n_eff is the effective duration of the resonance (typically around ten revolutions). ... Typically the extraction takes place near v = 0.8.

Heikkinen, Injection and Extraction for Cyclotrons — CAS, CERN 94-01 (1994) — p. 14

Tabletop: A classical (weak-focusing) machine never has nu_r>1, so create the amplitude by ion-source off-centering instead and use the same nu_r~0.8 fringe region for precession.

the spreading of orbit centres for different HF phases due to HF mixing, is small for an originally well centreed beam, as in general the number of turns from the vr = 1 resonance till extraction is not so large.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 9

Tabletop: If a next machine uses source off-centering (amplitude created at turn 1), expect full phase mixing over 30-100 turns: the amplitude survives but its direction smears - a trim bump near the extraction region is cleaner.

PIG ion source 10-50 [energy spread, V] 5-500 [typical ion current, mA] (Table 2.1)

Wolf (ed.), Handbook of Ion Sources (1995) — p. 51

Tabletop: A 10-50 eV spread against a few-keV first gap is a phase-space nonissue for the reference machine; do not trade source simplicity for energy spread.

the plasma temperature that provides the best match for experimental beams is approximately 35,000 K (resulting in a central starting energy of 4.5 eV)

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 3

Tabletop: Drop-in starting condition for the reference machine's central-region orbit models — start protons at 4.5 eV from a flat sheet across the slit, not from rest at a point.

Post-to-foil transmission increased dramatically (from 19% to 30%) but the total target current decreased from 120 uA to 40 uA

Potkins et al., Improvements to Siemens Eclipse PET Cyclotron Penning Ion Source (2017) — p. 3-4

Tabletop: For a machine starved of axial acceptance a hole source wastes less injected beam, but total current favors the tall slit. The weak-focusing reference machine with a 1.5" gap has generous axial acceptance — use the slit.

produced a field of 96.7 percent of this value at 96.5 percent of the total radius (corresponding to the magnetic index n = .2), with an approximately linear decrease in field from center to edge.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9-10

Tabletop: Directly applicable weak-focusing target - same n=0.2-class profile is the textbook goal for an 8-inch fixed-frequency machine's shim program.

The autographs indicate a rapid spreading vertically of the beam at about 81 1/2 inches. This agrees quite closely with the point at which n = 0.2 from magnetic measurements.

Vale, 184-inch Cyclotron Vertical Beam Oscillations in the Region of 82-inch Radius — MDDC-984 (1947) — p. 3

Tabletop: Fully applicable to fixed-frequency machines: map B(r) on the bench, compute n(r), and put the target/septum radius inside the n = 0.2 point; if the reference machine's beam stalls early, this is suspect number one.

in an effort to determine more definitely that the peaks, or 'pips,' shown in synchroscope photographs of the beam current are caused by precession of the beam.

Yeater, 184″ Cyclotron: Synchroscope Beam Pictures on Two Probes — MDDC-987 (1947) — p. 3

Tabletop: The FM pulse envelope is synchro-specific, but the two-azimuth probe comparison transfers: any structure that keeps a fixed phase relation between azimuths is orbit dynamics; anything common-mode is source or RF fluctuation.

Approximately 60 kv could be held on the high voltage electrode of this deflector.

Sewell, 184″ Cyclotron: Vertical D.C. Electrostatic Deflector — MDDC-1051 (1947) — p. 2

Tabletop: A next machine needs only a few kV/cm over a few cm of channel - an order of magnitude below what 1947 in-tank hardware sustained, so deflector voltage should not be the limiting risk; the series resistor for spark current limiting is worth copying.

accelerating particles past the radius where n = 0.2 in the 184-inch cyclotron has been postponed, since the available energy of the ions at this radius is within 5 per cent of the maximum of the system

Sewell, Henrich & Vale, Some Operating Phenomena Associated with the 184-inch Cyclotron — MDDC-1092 (1947) — p. 4

Tabletop: Budget a next machine's energy at the n = 0.2 radius, not the pole edge; shaving the pole-edge shims to push n = 0.2 outward buys more usable energy than chasing radius into the fringe.

It must be kept in mind for systems having low accelerating voltages similar to the 184-inch cyclotron, that the ions will rapidly increase the amplitude of their vertical oscillations at the point where n = 0.2.

Sewell, Henrich & Vale, Some Operating Phenomena Associated with the 184-inch Cyclotron — MDDC-1092 (1947) — p. 4

Tabletop: The reference machine's few-kV dee means thousands of turns - the explicit worst case named here; keep dee aperture at least twice the expected radial oscillation amplitude and keep n < 0.2 over the whole usable radius.

The frequency of the minor pulses in each beam pulse agrees quite well with the calculated frequency of precession of the center of rotation of the ions about the magnetic center of the system

Sewell, Henrich & Vale, Some Operating Phenomena Associated with the 184-inch Cyclotron — MDDC-1092 (1947) — p. 4

Tabletop: Transfers with caveats: on a CW fixed-frequency machine you need a pulsed source or fast probe electronics to see the structure, but a pulsed-arc mode run makes precession directly visible on a scope.

Field drop-off 3-4 %

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 164

Tabletop: Directly transferable target for shimming the reference machine's 0.59 T field: a measured 2-4% drop across the usable radius, smooth and monotonic, is what the entire fixed-frequency population converged on.

Internal Beam, Stable, ua 1000-2000 ... External Beam, Stable, 800 ua; 100 ua focused on target 15 ft from machine

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 107

Tabletop: If the reference machine sees nA, the gap to the historical uA-mA norm lives in source output and center-region transmission, not physics limits - and even good 1950s machines lost most of the beam at extraction, so budget a next machine's external current pessimistically.

Beam defining slits used on 1, 2, and 3rd revolutions to define center of beam rotation; 3rd turn slit is 1/2 mm wide. 100% extraction efficiency with low beams, requires better than 1/2 % stabilization of dee volts.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 27

Tabletop: The cheapest extraction upgrade known: mechanical slits in the center region plus tight dee-amplitude regulation; for a next machine's turn-separation budget, orbit-center definition on turns 1-3 matters more than deflector finesse.

Electric focusing with carbon grids on the dees successful on first four revolutions

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 27

Tabletop: First-turn loss at low dee voltage is a classic tabletop failure mode; a fine grid (or slit plate) on the dummy-dee aperture is a proven 1950s fix that costs an afternoon to try.

It minimizes electric defocusing, which is ordinarily a major cause of beam loss, and actually provides some focusing during the usually defocusing part of the phase excursion.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10-11

Tabletop: The reference machine's beam losses in the first turns are exactly this mechanism at nA scale; a flat-topped dee is likely too much RF plumbing for a next machine, but the rule explains why phase excursion and gap-crossing timing dominate small-machine transmission.

the same bunching occurs even if a third harmonic is added to the r-f wave form to square the wave

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10

Tabletop: Reassurance that waveform shaping and center-region bunching are separable problems; also a reminder that the bunching mechanism itself (Cohen) is what sets which ions survive the reference machine's center region. OCR note - theta prints as (c) in these appendix equations.

the radial displacement amplitude is equivalent to about twenty turns, or to about two kilovolts, or about 1% spread in energy at the exit radius

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 12

Tabletop: Sets the physics floor on energy spread from central bunching for any future extraction work; at the reference machine's and a next machine's energies the effect is small in absolute mm but the ~1%-class energy-spread scale is exactly what a deflector/slit design must budget for.

A major improvement was effected when an off-center source was installed which injected azimuthally into one of the dees.

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 12

Tabletop: The geometry lesson is scale-free even though these are milliamperes of internal beam - a doubled capture fraction and cooler dee tips from source position/orientation alone; for the reference machine's filament source, radial position and slot azimuth are cheap, high-leverage experiment variables (directly relevant to a planned source-species test).

the high-voltage electrode should have the minimum possible surface area. This minimizes the amount of sparking required to bake out the cathode spots and reduces the amount of electrode contamination.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 16

Tabletop: Directly. Measure the next machine's beam height at extraction radius, size the deflector field window ~2x that, and keep the HV bar as small and short as the trajectory allows.

the increase in radius of the burst of ions per rf cycle is approximately 0.1 inches and the deflector bars are spaced one inch apart, the pulse must occur within +/- 5 rf cycles.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 8

Tabletop: Synchrocyclotron-specific hardware (a next machine's CW deflector needs no pulse), but the requirements chain - turn separation sets element aperture sets timing/rise budget - is the template for sizing ANY extraction element, including the next machine's septum entrance.

The extraction requirements, simply stated, are: (a) The precession must be arrested (b) Sufficient gain per turn must be obtained (c) Losses owing to axial blowup must be minimized.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 7

Tabletop: The cleanest checklist in this collection for what a next machine's precessional-assist extraction must accomplish - phase-lock the precession to place orbit maxima at the septum azimuth, then count gain-per-turn against septum thickness. Machine-class independent.

The synchronous radius suitable for deflection in the cyclotron is just inside the radius at which normal beam destruction occurs.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 7

Tabletop: The siting logic transfers even though the numbers are synchrocyclotron pole-edge values - put the next machine's septum/regenerator equivalent just inside where the field map says the beam dies (n -> 0.2 walkout or resonance), and know that every mm inward is energy given away.

The determination of the required perturbation for extracting the beam of a synchrocyclotron is made in seven steps.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 6

Tabletop: The workflow (measured field -> amplitude-dependent tunes -> impulse-matrix tracking -> element strength) is exactly the CYCLOPS-lite pipeline planned for a next machine; the specific peeler-regenerator field shapes are synchrocyclotron machinery and need not transfer.

For a 1-in. axial amplitude this disturbance is about twice as strong as that occurring in the radial motion from the same field perturbation.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 18

Tabletop: The general warning transfers - any radial-field-gradient extraction element has an off-midplane Br that pumps vertical motion, so check axial kicks in the next machine's tracker for the deflector fringe and any field bump, and expect to lose the large-axial-amplitude tail first.

It is an advantage to choose the smallest value of l, since the choice allows the least sensitivity in matching the perturbing frequency to the particle motion.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 7

Tabletop: A genuinely tabletop-compatible extraction assist - an electrode pair driven by a small independent oscillator. For a next machine (nu_r ~ 1) the required frequency is near the orbital frequency's sidebands; worth a tracker experiment before committing hardware.

In the weak vertical field component of the accelerating voltage in the 184-inch cyclotron the beam loss was impressively fast.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 5

Tabletop: A real design caution at any scale - dee misalignment or asymmetric liners give exactly the z-proportional E_z this resonance needs. Keep a next machine's dee/dummy-dee vertically symmetric and check whether nu_z resonates with any strong rf harmonic at operating field.

because of the precession of orbits all particles are ultimately perturbed to larger radial oscillation amplitudes.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 9

Tabletop: Sets expectations for any resonant/precessional scheme on a next machine - extraction is a many-turn statistical process, so judge schemes in the tracker by turns-to-extraction and septum-hit fraction, not single-pass kick size.

The increase in proton energy resulted from relocation of the ion source 1 1/2" upward; the source is now effectively only one inch below the magnetic center.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 8

Tabletop: A 26% energy gain from moving the source — on the reference machine, treat filament/chimney height relative to the median plane as a tuned parameter worth systematic scans, not a set-and- forget dimension. Symmetric placement about the magnetic (not mechanical) midplane is the target.

the beam striking the periphery of the south dee. This condition resulted from the center of rotation of the beam being offset to the south by a distance of approximately three inches.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 7

Tabletop: Fully transferable — witness marks on the reference machine's dee edges and probe shadows are a free orbit-centering diagnostic; an orbit center offset a few percent of pole radius is normal and correctable by moving source or dees.

most of the loss of protons to the dees occurs during early revolutions. Only a small percentage of the beam is lost beyond one-half of maximum radius, Figure 5.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 16

Tabletop: Both the finding and the instrument transfer: stack 3-5 insulated foils as a segmented z-probe on the reference machine to see where the beam sits vertically, and spend tuning effort on the first turns — beam surviving to half radius will almost all reach full radius.

an increase in bias potential on the dees increases the beam accelerated to maximum radius by a factor of as much as 30% when the cyclotron is operated without an accelerating slit (rf) mounted on the dee.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 16

Tabletop: Worth a cheap experiment on the reference machine (a DC bias supply on the dee), but the ORNL conclusion is that geometric phase selection (a slit) beats electrostatic tricks — put the effort into the puller/slit geometry first.

It was found that distortion of the magnetic field when the tank is evacuated is negligible. Latest measurements of the magnetic field reveal a first harmonic inhomogeneity of approximately 0.03%.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 15

Tabletop: Two transfers: verify a next machine's field map with the chamber assembled and pumped (pole deflection under vacuum load is a real 1950s worry that proved negligible for them — measure once to confirm); and note 0.03% first harmonic as what a carefully shimmed classical machine actually achieved — consistent with the ~5 G field target for a next machine.

Current measurements beyond 18.5" were unreliable; the current at the maximum radius, 25.5", is estimated to be of the order of one microampere.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 10

Tabletop: Calibrates expectations for the reference machine's and a next machine's first runs — nA at full radius from uA-class first-turn current is what a real machine did at first beam; log the whole I(r) curve, because its shape (where the loss happens) is the tuning roadmap.

the ion source position is limited to a maximum radius of 2.5 inches. This forces operation at comparatively low dee voltages (20-30 kv) in order to center the orbits.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 5

Tabletop: The design logic transfers directly to a next machine's central-region layout: pick dee voltage and source-puller radius TOGETHER from the first-orbit geometry. It also cuts the other way for the reference machine's 5-13 kV upgrade: raising dee voltage moves the optimum source position outward — re-scan source position after the RF upgrade.

The isochronous fields are obtained with trim coil settings computed by a linear program, and their greatest deviation from isochronism is less than 15 gauss in all cases.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Tabletop: A measured 1960s tolerance to calibrate the next machine's 5 G / 5-deg-RF-phase target against: an AVF machine accelerating hundreds of turns lived with 15 G deviation. A classical few-tens-of-turns tabletop machine tolerates proportionally more — the phase-slip integral, not the gauss number, is what to check in the tracker.

The starting conditions for all cases were estimated by starting the ions on an equilibrium orbit of 12 inch radius and de-accelerating them to the center.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Tabletop: Directly implementable in the Python orbit tracker — find the equilibrium orbit at modest radius (easy, well-conditioned), integrate backwards to the source region, and read off where the source slit and puller must be; cheaper and more robust than guessing forward launch conditions in the messy first gap.

the beam measured at extraction is augmented by possibly 10% by using 22 amps in trim coil number 1 rather than -145 amps. The former produces the central radial bump.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Tabletop: Validates the classical-cyclotron instinct for a next machine: a small positive field bump at center (field falling with radius from turn one) focuses the turns that the z-distribution studies (ORNL 22-inch) show carry all the loss; give away a little phase to get it. Empirically checkable on the reference machine with shim washers at the pole center.

The particles pass through the 3/3 resonance at a radius of 6-7 inches. The computer calculations show that the radial oscillation build-up at resonance is not excessive and soon damps to 0.3 inch.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Tabletop: Method for the CYCLOPS-lite tracker: don't just plot nu_r(r) and forbid resonance lines — integrate through them and report amplitude growth in millimeters against the aperture; a fast-crossed resonance with bounded growth is a non-event even on a small machine.

the validity of the calculations and magnetic field data is supported by the fact that we obtained an internal beam of 21 MeV H2+ ions using the computed field on the first attempt.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 7

Tabletop: The 1966 proof that a next machine's compute-first pipeline (field map -> tracker -> build) is sound — if the field is measured carefully and the tracker is honest, first beam on the first pump-down is a reasonable expectation, not luck. Also a period example of commissioning on H2+ rather than protons for shielding reasons.

This region, called the "gap," should have a diameter about nine times as great as its axial dimension.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 6

Tabletop: CORROBORATING, not new - the same premises underlie Livingston-Blewett and Wouters (corpus already carries 0<n<1 stability). TID-454's working condition is the stricter n<<1/5; note its own 130-in/14-in example is 9.3x. The reference machine's 8-in poles over a wide gap fall far short of 9x, which is exactly why usable radius is scarce; a next machine's gap choice should respect this proportion.

The operation of the oscillator determines the variation of capacity with time which will keep the ion phase constant. This variation is not very critical.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 152

Tabletop: Synchro-only for cyclotrons, but the pattern maps onto a small synchrotron's RF ramp - program tolerance is loose if phase stability (not exactness) is the criterion, and cycle dead time is a direct beam-current tax.

Measurements of the internal beam of the ORNL 86-inch cyclotron very early indicated that the energy of the proton beam might vary as much as +/-10% from H-rho calculations.

Cohen, Measurement of Beam Energy and Energy Distribution on an Internal Cyclotron Target — ORNL-1347 (1952) — p. 5

Tabletop: Verified on the page image, and the direct historical support for this collection's energy-convention discipline: the reference machine's "150 keV-class computed" is a convention, not a measurement. For a next machine's B11(p,alpha) work, where yield vs energy is steep, measure energy AT the target (absorber stack in front of the PIPS, or foil methods) every time tuning changes.

From (5) the measurement of dr is essentially a determination of the phase.

Cohen, Spatial Distribution of Current on an Internal Cyclotron Target — ORNL-1348 (1952) — p. 9

Tabletop: Table verified on page image. Energy-independent physics: on the reference machine or a next machine a differential probe (shadowed double tip) or the sectioned-target map gives dr, and with the known dee voltage that is a measurement of ion RF phase — the quantity a next machine's 5-G field tolerance is protecting. A rare direct experimental handle on phase for machines with no beam-position monitors.

leaving the ion source ungrounded has a very substantial effect, since it then floats nearer the potential of the accelerating slit which is attached to the dees.

Cohen, Spatial Distribution of Current on an Internal Cyclotron Target — ORNL-1348 (1952) — p. 9

Tabletop: Direct lesson for the reference machine's central-region debugging — the source body's DC potential is a real optics knob (or a real gremlin). Verify the filament/chimney ground path is defined and logged; an intermittent source ground would masquerade as day-to-day beam irreproducibility of exactly the kind ORNL-1347 warns about.

the ions which were the chief contributors to the current at resonance are lost by defocusing and ions of more positive phases are now the chief contributors.

Cohen, Spatial Distribution of Current on an Internal Cyclotron Target — ORNL-1348 (1952) — p. 9

Tabletop: Explains an observation class on the reference machine: probe current can look tolerant of field/frequency error while the beam's phase (and thus its energy at radius) shifts underneath — reinforcing ORNL-1347's rule that current on target is not evidence the energy is what B-rho says. Phase self-selection also broadens resonance-tuning curves; do not read their width as the true stability margin.

Six- and eight-sector machines are free from strong essential resonances ... also, the symmetry easily permits four accelerating gaps per revolution, a situation well suited to rf cavities.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 266-267

Tabletop: 810-MeV specifics (vr climbing to 2, spiral sectors) do not scale down; the method — list resonances crossed by your vr/vz trajectory before fixing N, then let RF layout break ties — applies to any AVF design.

electric fields are relatively ineffective at high particle velocities, but the force on an ion due to a magnetic field is proportional to velocity.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 151

Tabletop: At 150 keV protons (v ~ 5e6 m/s) the comparison runs the other way — modest electrostatic septum fields are equivalent to impractical coil fields — so amateur-scale extraction stays electrostatic; do this arithmetic before copying any big-machine magnetic channel.

When the horizontal component of the geomagnetic field was canceled, this attenuation was eliminated.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 276

Tabletop: Their Analogue ran at 42 gauss central field, where Earth's ~0.5 G matters; irrelevant inside the reference machine's 0.59-T gap but real for any low-field electron-analogue experiment or long low-field injection path.

The data show individual orbital positions from the first orbit up to the twelfth, the upper limit being determined by the potential on the dees.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 December 1951 — ORNL-1269 (1952) — p. 40

Tabletop: Directly runnable on the reference machine with the existing probe hardware - measured turn spacing would convert the "~800 V nominal, uncalibrated" dee voltage into a calibrated energy-gain-per-turn number. Fig. 12 (PDF p. 41) shows the machine doing this at 9.2-12 kV dee-to-dee with 600 V dee bias.

a choice of radius, 11 in. or 20 in., is thus obtained by shifting the position of the dees and target. In either case the ion source position remains unchanged and the beam orbits remain centered

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Tabletop: Variable energy WITHOUT retuning B or rf - since E ~ r^2 at fixed field/frequency, a repositionable target (or dee assembly) gives an educational machine two calibrated energies for the price of one; the invariants to protect are source position and magnetic centering, exactly as ORNL did.

Plans are being made for an electron-model accelerator to be used in assessing the importance of imperfection resonances and the feasibility of their penetration.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 35

Tabletop: Historical validation of an electron-model approach and of risk-ordered development - when the open question is orbit dynamics (resonance crossing, field tolerance), a tabletop electron machine answers it before proton iron is bought. (Same page — Thomas-1938 AVF theory, ORACLE computing, MURA spiral sectors - sector focusing arriving in this collection's timeline.)

in order to produce a suitable object for the analyzing magnet, we introduce a second magnet whose sole function is to focus as much of the beam as possible on a precision slit.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 4

Tabletop: DIRECT - this is the canonical two-stage architecture for any external line on a next machine. The optical condenser/analyzer analogy (illuminated slit as object) is the cleanest possible statement of why "focus first, analyze second" beats one clever magnet.

A considerable amount of undesirable radiation will be produced by that part of the beam intercepted by the slit system.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 5

Tabletop: DIRECT and cheap to honor at layout time, nearly impossible later. Even at 150-170 keV the slit is the hottest x-ray point on the line (thick-target bremsstrahlung at full beam power); a next machine should treat every defining aperture as a shielded component.

the weight and power requirements would each be less than the corresponding sector-magnet requirements by at least a factor of ten.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 6

Tabletop: DIRECT - the as-built comparison (p.32) was 355 lb for the doublet pair vs an estimated 3 tons for a sector condenser. At a next machine's rigidity (~7x lower than Rochester's 4e5 G-cm) a doublet becomes a benchtop object; the no-deflection tunability argument is the one to remember when laying out the line.

the effective "point" source in the vertical plane does not coincide with that in the horizontal plane and is such that the vertical-plane object distance V is greater.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 14

Tabletop: DIRECT design input for any next-machine transport modeling - the tracker should fit separate horizontal/vertical source points from measured beam profiles rather than assume a stigmatic waist at the extraction channel.

With this as a guide we apply an extra factor of safety and take a = 3, c = 1.5, hence the magnet poles are given by xy = +/- 2.25 cm^2

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 29

Tabletop: DIRECT method (not numbers) - measure the real beam first, then stack two explicit margins. A next machine's envelope must come from its own extraction simulations/measurements; the 50%-then-round-up discipline is what prevents an undersized bore discovered after winding.

Measurements have shown that the effective length of the magnets is as much as 20% greater than the physical length.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 29

Tabletop: DIRECT - for short quads the fringe extension is a first-order effect, not a correction. Modern practice: l_eff = l_phys + ~aperture radius; get it from the FEMM/tracker pipeline per magnet, and expect focal errors of tens of percent if ignored.

For fields above about 8 kilogauss, saturation effects begin to set in, and the field becomes less uniform near the pole boundaries.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 43

Tabletop: DIRECT sizing rule with scale caveat: the 8 kG threshold is geometry- and steel-specific, but the logic (uniformity budget, not raw B_sat, sets the working field; bend radius follows) applies to any analyzer dipole on a next machine. At ~170 keV protons rho is a few cm even at modest fields - the analyzer becomes a bench magnet.

The effect of the fringe field is to shift the effective pole boundary outward, and this is taken into account empirically by adding to the right-hand side of III-20(b) a term 0.4 G

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 43

Tabletop: DIRECT - the 0.4-gap effective-boundary shift is the same magnitude modern codes assign (FINT*gap); for a next machine's analyzer designed in FEMM the rule is a sanity check that the simulated effective edge sits ~0.4 gap outside the steel.

the methods for correcting for the fringe fields effects ... are not sufficiently precise to warrant basing the magnet design on the second-order calculations.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 50

Tabletop: DIRECT design-philosophy rule for the whole next-machine campaign - match model order to input-data quality. Also note the companion check they DID run (pp.49-50), that the bent beam clears the back of the magnet with ~5 cm margin for the full 6 cm beam - a 30-second calculation that catches a catastrophic layout error.

The operation of the wedge analyzer has been checked using the standard current carrying wire technique.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 52

Tabletop: DIRECT trio of transfers: (1) budget alignment/tuning provisions into any multi-element line; (2) the floating-wire method (wire under tension carrying current I follows the trajectory of a particle with B-rho = T/I) is a superb zero-beam teaching-lab measurement of magnet optics; (3) their bottom line - 0.1 uA on target at ~0.2% energy spread (p.53) - is the achieved-performance benchmark for a first-generation small-machine analyzed beam.

the problem of obtaining a pulsed beam usually does not arise, because the beam of a conventional cyclotron is already naturally bunched.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 6

Tabletop: DIRECT and foundational for the experiment catalog - every cyclotron, including the reference machine at 9 MHz, delivers ~10-40 degree phase bunches at the RF period. The bunch structure is a measurable, teachable property (phase width vs turn number) and the enabling fact for every timing experiment on the machine.

In our case reducing the frequency of beam pulses to about 3 mc can virtually eliminate the problem.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 16

Tabletop: SCALE-HONEST: frame overlap needs multi-MeV spectra over meter paths, so sub-MeV machines rarely hit it - but the tool is general: a pair of deflection plates driven at an RF subharmonic is the cheapest beam chopper a cyclotron can have (single-bunch selection, duty-cycle control, background gating), and the odd/even zero-crossing subtlety is real circuit-level physics worth teaching.

the acceleration can be considered to good approximation as being a simple impulsive change in the energy of the particle at the azimuth of the accelerating gap

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 4

Tabletop: The core architecture for CYCLOPS-lite — thin-gap kicks alternating with magnetic coasting maps is 1961-validated practice, and MSUCP-12's analytic gap field upgrades the kick from a delta function to a distributed one when transit time matters.

The Fixed Point Code locates closed orbits by means of a highly effective linear transfer matrix procedure, the General Orbit Code tracks arbitrary orbits as desired

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 5

Tabletop: This is the CYCLOPS architecture in embryo (the lineage the planned "CYCLOPS-lite" copies); a next machine's tracker should likewise separate the equilibrium-orbit /tune solver from the general tracker, sharing one Fourier-vs-radius field representation fed by FEMM.

the general orbit code is employed to trace forward and backward in time orbits with initial conditions displaced slightly from the unstable fixed points.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 5

Tabletop: Directly reusable in a Python tracker (integrate with negative dt for the backward branch); the efficient way to draw the r-pr stability picture of any field candidate for a next machine near resonances.

the small axial beam space in a cyclotron constrains the particles to move in a region where the z dependence of the field is quite linear.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 3

Tabletop: Permission to build the next machine's first tracker 2-D (r, pr, E, phase) and add axial motion as a linearized afterthought — with the same obligation to verify by a handful of full-3D spot checks.

The powerful effect of a cos 0 field component in a cyclotron ... is clearly evidenced by the large changes in the phase plot which result when the small 1% bump is added.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 22

Tabletop: Cuts both ways at reference-machine and next-machine scale — shim asymmetries of tens of gauss are dynamically significant near nu_r = 1 (center and full radius), yet a deliberate few-turn bump coil is a powerful, cheap orbit-steering experiment.

introduction of the field bump has caused a discontinuous jump in the location of the central stable orbit in the phase diagram

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 24

Tabletop: The conceptual mechanism to have in hand before any extraction attempt on a next machine; it needs nu_r to pass unity with a controlled first harmonic — both quantities a FEMM-fed tracker can compute for a candidate pole design.

stretching and rotation are fine but not twisting, filamentation, etc.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 24

Tabletop: The right figure of merit for any next machine's beamline or extraction simulation — track a small grid of particles and judge the deformed shape, not just the centroid; five to two dozen particles sufficed in 1961.

The essential design requirement of such a system is a turn program which avoids regions of large flow rate gradient in the static phase space.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Tabletop: The doctrine transfers whole to any resonance-crossing scheme on a small machine — cross fast where the map is ugly; the diagnostic (superimpose the accelerated beam path on static phase plots) is a cheap tracker post-processing step.

volts per turn substantially lower than the designed 280 kev/turn would result in sharp reduction of both extraction efficiency and optical quality.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Tabletop: The quantitative ancestor of "dee volts buy extraction" — the reference machine's ~800 V nominal dee is why it is internal-beam-only, and the next machine's 5-13 kV target is what would make any future extraction scheme even thinkable.

The sinusoidal voltage, it is seen, shifts the final position of the beam spot but has almost no effect on the distortion.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 40

Tabletop: A permission slip for CYCLOPS-lite staging — start with constant energy gain per gap to get the radial dynamics right, then add cos(phi) gain and phase slip as a second-stage refinement, checking that conclusions survive.

the result is seen to fairly accurately predict the actual amplitude and 0 of this point of the grid

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 44

Tabletop: Two lessons — build point analytic cross-checks into a next machine's tracker test suite (transfer-matrix estimates vs tracked orbits), and note the physics is benign for a 180-degree-symmetric two-dee tabletop field where the paired kicks cancel.

This paper presents in summary formulas for the computation of electric fields and potentials of an idealized cyclotron dee geometry.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 6

Tabletop: TRACKER SEED (flagged): this is directly implementable as the gap-field model in the tiny and the next machine's Python trackers — roughly ten lines plus a Newton solve — replacing or validating FEMM electrostatic maps. Identify 2h with the dee aperture, 2k with the dee-to-dummy-dee gap, 2V0 with the full dee-to-dummy-dee voltage (a grounded dummy dee is the same solution shifted by a constant, V0 = V_dee/2).

Therefore, equations 2 and 4 coupled with equations 3 and 5 can be used to determine the electric field and potential at a point X, Y of the dee region.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 5

Tabletop: E_y(x,y) is exactly what a tracker needs for the Rose/Wilson electric gap-focusing term that dominates axial stability on the first turns of a sub-kV machine like the reference machine — available here analytically at any (x,y), no field map required.

Table 1. k/h = 0.1: at x/h = 0, E/(V0/h) = 0.99388 [values verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Tabletop: Sets the real ceiling on gap-field strength for any dee redesign — with a 1-inch aperture (h = 0.5 in) and 5 kV dee-to-dummy (V0 = 2.5 kV), peak field cannot exceed ~2 kV/cm no matter how tight the gap; widening the aperture for beam height costs peak field one-for-one.

Table 1, k/h = 0.1: V/V0 = 0.73760 at x/h = 1.0, 0.94468 at 2.0 [verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Tabletop: Transit-time factors and gap-crossing phase errors for the tiny machine and a next machine must be computed on this extended profile — at low first-turn velocities the particle spends a large RF phase interval inside a field region ~2h long, which a delta-kick model at the gap centerline gets wrong.

The process is a trial and error search, with general guidelines and test criteria for success.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Tabletop: Directly transferable design-process pattern for any pole/shim work on a next machine — let FEMM play the role of the Nevis model magnets, with analytic tune formulae as the accept/reject criteria instead of a target field profile.

first evaluated using the Smith-Garren formula, checked at critical places, especially at larger r, by exact orbit motion computer solutions.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Tabletop: Exactly the field-solver-plus-orbit-tracker pipeline an amateur design can run; the Nevis precedent says spend the expensive tracking only where the cheap formulae are least trustworthy.

alerted by the ORNL studies of observed beam loss in the ORIC cyclotron to try to avoid

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 4

Tabletop: Method transfers directly — a tune plot should carry resonance lines sourced from operating-experience literature, not just textbook theory; a weak-focusing tabletop crosses fewer lines but the audit habit is the point.

a slow linear reduction (turn off) of the RF amplitude there will result in a near adiabatic spreading out of the phase angle

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Tabletop: Meaningless for a fixed-frequency CW tabletop cyclotron; it belongs to swept-frequency machines, where adiabatic capture and slow parameter ramps are the RF-program design space.

It has always bothered me that a film should ever break at its thickest port [sic]; (Ramsay, "Alternatives to Thin Film Carbon Foils")

Fifth Annual Conference of the International Nuclear Target Development Society — LA-6850-C, Los Alamos Scientific Laboratory (1977) — p. 81

Tabletop: Any thin internal target or probe foil in a proton beam fails by this stress mechanism long before bulk melting; inspect failed foils for the radial-crease signature before blaming heat.

the foil breakage time is dependent on the total number of bombarding ions (Livingston, Berry & Thomas, "Thin Carbon Foil Breakage Times Under Ion Beam Bombardment"; reprint of NIM 148 (1978) 125)

Proceedings of the Sixth Annual Conference of the International Nuclear Target Development Society — LBL-7950, Lawrence Berkeley Laboratory (1978) — p. 152

Tabletop: A fluence budget, not a current limit — halving the current doubles the time to the same death; plan foil replacement by integrated charge, and never buy life by thickening a foil.

If the beam is focused to an area of about 0.2 cm2, the resulting specific energy depositions amounts to 1 kW/cm2.

International Nuclear Target Development Society Workshop — ANL/PHY-84-2, Argonne National Laboratory (1983) — p. 29

Tabletop: The reference machine at -3 nA / ~150 keV deposits ~0.5 mW — any target survives. The same two-line arithmetic must be rerun at every upgrade; a 10 uA / 1 MeV machine puts 10 W into a mm-scale spot, and that is rotating-target or water-cooled-backing territory.

target heating can be a problem and efforts are made to diffuse the beam on the target.

International Nuclear Target Development Society Workshop — ANL/PHY-84-2, Argonne National Laboratory (1983) — p. 58

Tabletop: The zero-cost cooling knob — spot size enters the W/cm^2 arithmetic squared. For activation or yield runs on a small machine, defocus or wobble the beam before engineering any water cooling.

thermal runaway would occur and the stored beam would be lost.

International Nuclear Target Development Society Workshop — ANL/PHY-84-2, Argonne National Laboratory (1983) — p. 218

Tabletop: Directly relevant to the synchrotron campaign, not the cyclotrons — any internal-target idea for a ring must respect the multiple-traversal multiplier, which turns nanoamp circulating currents into effective milliamp bombardment.

The properties of a magnetic field in space make it impractical to obtain a properly shimmed field if the gap length is much greater than one-half the radius p.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 12

Tabletop: An 8-12 in. pole with a 1-2 in. gap sits far inside this limit, which is why small cyclotron shims work at all; the rule bites for any short-radius bending/analysis magnet where a generous gap is tempting for access.

is the maximum allowable space rate of change of the magnetic field in a direction toward the edge of a gap.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 15

Tabletop: The general move — translate a beam-geometry tolerance into a measurable dH/dx budget via the curl-free midplane relation — is machine-independent and gives a field-map pass/fail number before any tracking is run.

it was necessary for the values of the quantity integral h_z dx, experimental and theoretical, to differ by less than 3 cm, in terms of galvanometer deflection.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 87

Tabletop: The discipline transfers whole: derive numeric field-map acceptance bands from orbit tolerance (phase-slip or centering budget) beforehand, so a survey ends in pass/fail per region instead of open-ended interpretation. Orbit-integral quantities beat point values when the beam only feels the integral.

A magnet of this size when used with detuerons, is about the optimum dimensions in which deuterons may be accelerated profitably without resorting to frequency modulation.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 5

Tabletop: Any tabletop proton/deuteron machine sits far inside the fixed- frequency regime — phase slip there is set by field shaping and dee voltage, not relativity, so FM hardware is never the fix for small-machine beam loss.

(1) in the median plane the variation of the intensity with radial distance must conform closely to a fairly well defined relation, and (2) inside the exit radius ... the field must be accurately symmetrical

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 14

Tabletop: DIRECT — the same decomposition (radial law, azimuthal symmetry, median-plane flatness) is how a tabletop field survey should be organized, each with its own instrument and its own fix.

The function of the spikes is to produce a sharp increase in the induction at the center of gap without producing a minimum anywhere in the radial dependence.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 33

Tabletop: A central field bump gives axial focusing in the first turns, where small machines lose most of their beam. A machined center button is one of the cheapest beam-current experiments available to the reference machine or a next machine — the no-minimum constraint is the part that takes care.