Modeling design rules

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.

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.

it was not possible to operate the model magnet at the extremely low (3.5 kilogauss) field levels at which we might like to operate the full scale machine.

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: Modern translation for the FEMM pipeline: a model (physical or FEM) validated at one excitation does not certify another — iron saturation state changes the profile shape, so re-run the field solution at every planned operating point, especially the lowest, and verify the real magnet across its full excitation range.

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 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.

The push-pull circuit for this test was constructed by using an 8-ft section of the electrical model of the 63-in. cyclotron dee stems as the resonant system.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 19

Tabletop: A bench-scale dee-stem mockup (pipe sections plus padding capacitors) lets the next machine's oscillator/coupling scheme be raced against alternatives for pocket change - the same measure-on-model philosophy as the deferred filament-coupling rule, one report earlier in hardware form.

The pole tips are removable so that shims of any shape can be inserted readily.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1954 — ORNL-1795 (1954) — p. 19

Tabletop: For any next-machine shim-test rig (or a scaled FEMM-validation magnet), design for the measurement campaign - open sightlines for the Hall probe, pole tips that unbolt, gap oriented for jig access. ORNL judged these features worth 14.4 tons of model.

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.)

Performance of the model is considered sufficiently satisfactory to proceed with the full scale design and construction based on the model dimensions.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 16

Tabletop: A next machine's dee/stem/tank is already benchtop-sized, so the transferable form is the mockup itself — a cheap RF-only copy (no vacuum) of the dee-liner geometry, swept with a VNA before the vacuum parts are machined. Same lineage as UCRL-64 and MDDC-1045 already in this collection.

Only the radio frequency circuit was simulated in the model, the vacuum system and purely mechanical equipment was not included.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 7

Tabletop: License to mock up the next machine's RF cavity in bare copper/aluminum on a bench plate — no chamber, no pumps — provided every conducting surface that carries RF current (liner included) is reproduced.

For 30 kv on the full scale system the above power input figures become 146 kw at 9.25 mc, 132 kw at 12 mc, 146 kw at 15 mc, and 98 kw at 23 mc for continuous operation.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 15

Tabletop: The V^2 term is the live part for a next machine's power budgeting — measured drive power at a safe low dee voltage extrapolates as (V_target/V_test)^2 on the same hardware, since Q is voltage-independent until multipactor/breakdown; a 1500-V measurement predicts the 5-13 kV LDMOS requirement.

the inductance inherent in the 304-TL triodes is large compared with that in the 9C21 triodes to be used in the final oscillator.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 12

Tabletop: When bench-testing a next machine's RF with a stand-in amplifier or without the real chamber wall, write the fidelity caveats into the test log — the model predicts the cavity, not the parts that were substituted.

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 radial spacing of the table entrys is interpreted as increased by the factor 64/8.75 corresponding to the ratio of pole diameters

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 6

Tabletop: The historical analog of the CadQuery->FEMM->field-map pipeline, plus two habits worth copying — symmetrize and smooth measured maps before tracking, and document every cleanup applied to the field the tracker actually ate.

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.

beams entering the extraction region approximately centered on the equilibrium orbit behave as well or better than beams entering with substantial displacement.

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

Tabletop: The project-level lesson for a next machine — run the cheap simulation before committing hardware to any orbit-dynamics intuition, including intuitions published by people as good as Blosser and Gordon.

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.

This iteration is Newtonian in character such that if a given X1 has an error of order e, then X1 given by equation 9 will have an error at order e squared.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 7

Tabletop: Copy the iteration and its initial-guess branch verbatim into the tracker's field routine; a handful of iterations reaches machine precision, cheap enough to call per integration step (or use once to build a spline).

Table 1 gives values of electric field and potential for a wide range of dee gap arrangements. [tables span PDF pages 11-19]

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

Tabletop: Unit-test targets for the tracker's gap-field routine AND an independent check on FEMM electrostatic runs — model the same idealized geometry in FEMM once and match these 5-digit values before trusting FEMM on the real next-machine electrode shapes.

A fixed point computer program written by D.A. Johnson for use on MISTIC was used to calculate the above equations for Ex and Vx at the point (X,0) with a<4.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 8

Tabletop: For use on a next machine, the real deviations to check against FEMM are finite dee thickness, the rounded/blunted tip, and the curved gap line near the source at small radius — expect the analytic solution to be excellent at mid-radius and approximate near center where the ion-source chimney dominates the field anyway.

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.

The design has used a 1/2 scale model, in conjunction with detailed computer calculations, to establish all parameters which can be varied

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 9

Tabletop: At tabletop size the "scale model" is the full-size mockup on the bench — cold-test a next machine's dee/stem with a VNA before power exists; the mode-spectrum audit transfers verbatim.

The value of mu used was found experimentally by measuring the field from a precisely known configuration of conductors

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 13

Tabletop: A model-calibration pattern the FEMM-based pipeline should copy — one deliberate known-geometry measurement (a wire loop, a known coil) in the actual gap pins the permeability/saturation assumptions the whole field model rests on.

The Q of the model will be 0.7 times the Q of the actual installation and so will require 1.4 times as much power for a given dee voltage.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Tabletop: Bench-model a dee-stem or resonator geometry at reduced size before cutting full-size copper; apply the sqrt(scale) Q correction before comparing model power and coupling measurements to full-scale predictions.

It was not excited satisfactorily due to the fact that at 100 megacycles the transit time effects were quite noticeable on the fundamental mode.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Tabletop: Cold measurements (network analyzer) scale exactly, but any POWERED model test needs a driver whose parasitics and transit time scale with the geometry, or the model will exhibit modes the real system never sees and vice versa.

dimensions can be calculated fairly exactly whereas in the system shown in Figure 5 one must depend on model tests (which are safer anyway).

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Tabletop: Transmission-line formulas ignore end effects, bends, and support hardware; for any resonator whose geometry is not a textbook line, a cheap model measurement outranks the calculation it checks.

The 1/2 scale model uses about 400 watts input to the oscillator at 48 megacycles and 600 watts input at 18 megacycles to produce 1500 volts on the dee.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 16

Tabletop: Dee power scales as voltage squared - measure watts-per-volt-squared on the bench, correct for Q, and the amplifier requirement for any target dee voltage falls out; joint quality and surface material shift Q enough to budget for.

It was desirable to know the magnetic field accurately to within 0.5 in. on the full-scale magnet. This corresponded to 1/32 in. on the models.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 73

Tabletop: The active-area rule for Hall mapping a shim edge: a 1-2 mm sensor is marginal where the gradient scale is a few mm (pole edge, shim step); position repeatability of the mapper jig belongs in the same error budget as the sensor.

a linear scale model built from steel with the same magnetic properties as planned for the prototype magnet and operated at the same field strength will give results directly applicable to the prototype.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 25

Tabletop: The physics that lets FEMM stand where models stood — and the terms of validity are the same for both: correct B-H data and correct geometry. Any cheap sub-scale mock-up of a planned magnet obeys it too, provided the steel matches and B is held, not NI.

since the X Beta model was built to 1/8 scale it seemed true that the results would be more accurate than those which could be obtained on a 1/16-scale model.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 149

Tabletop: The mesh-refinement decision in physical form — coarse resolution for excitation/force/leakage questions, fine resolution only for the ppm-level uniformity region; spending fine-model effort on questions the coarse model already answers is waste in either medium.

The usual measurements made included a magnetization curve, a comparison of gap performance at different points in the magnet, uniformity contour maps, determination of magnetic forces, the density of flux through various parts of the magnet

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 26

Tabletop: A ready-made deliverables checklist for a simulation campaign on a new magnet — a FEMM study that produces these five plots plus a member-by-member flux audit has done what the 1944 model program did, in the same order.

With 3400 oersteds in the gaps the efficiency obtained was 95.4 +/- 2.0 per cent. Within experimental error they were the same at both field strengths. This indicates that the magnet design is rather conservative.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 140

Tabletop: A two-point excitation scan (measured or simulated) separating "efficiency constant" from "efficiency dropping" localizes saturation onset without any interior probe — directly usable on an H-frame by comparing measured B vs I against the linear NI prediction at two currents.

In the neighborhood of 10,000 to 15,000 gauss the flux density is good, yet the yokes are not overloaded to the extent that the permeability of the steel drops excessively.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 141

Tabletop: The 10-15 kG working band for structural mild steel is the same number modern small-magnet guidance gives (cf. Wouters; Zickler CAS) — and the loop-audit method is the measurement twin of integrating B over member cross-sections in a FEMM postprocessor: every member gets a number, every number gets a verdict.

The permeability of the material of the full-scale unit is higher than that of the model. This indicates that a slightly better performance could be expected from the full-scale unit than from the model.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 146

Tabletop: The sign-audit habit transfers to simulation directly — list every model-vs-hardware difference (B-H table provenance, fillets, packing factor, gaps at joints) with the direction it biases the prediction, so measured-vs-predicted discrepancies arrive pre-explained.

The magnetic performance of the track is better than predicted from the model experiment.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 191

Tabletop: The historical calibration point for any predict-then-verify magnet pipeline: a faithful scaled model (same-steel/same-B then; validated FEM now) lands within a few per cent on global quantities and errs conservative when the prototype''s iron is better than the model''s — but the trust was EARNED by one full validation campaign, not assumed.

the excellent results obtained in testing track 1 showed that a dimensional check of the shim positions was entirely adequate.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 191

Tabletop: The economic payoff of validation: once field-vs-geometry is established (by model/simulation plus one measured article), later shim changes can be accepted on caliper and indicator readings, reserving full field maps for genuinely new configurations.

It would appear that the only feasible method of making corrections when the necessity arises is by trial and error.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 181

Tabletop: A 1944 warning that survives every FEMM run: analysis predicts the as-built field well but predicts CHANGES to an as-built field only if the change is modeled exactly as executed. Plan shimming as measure-cut-measure iterations, and keep shim stock adjustable.

the amount of testing required to arrive at a final shim design was much less than anticipated. This was due in part to the fact that the geometry of parts limited the possible variations more closely than was expected.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 17

Tabletop: With FEMM the model-magnet role is filled by simulation (ucrl-31 showed the scale-model method itself; MacKenzie AECD-1850 the model-test discipline), but the balanced verdict is the lesson — physical iteration budget should go where the computable model is least trustworthy (saturation, real steel, mechanical tolerances).

The steel for both the cyclotron magnet and the model was poured from the same heat and it can be assumed magnetic properties are identical.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 18

Tabletop: The transferable rule is identity of material between test article and final article — a next machine's FEMM model should use a B-H curve measured on the actual purchased steel, not a library curve for its nominal grade.

showed that the model data could be used as a basis of prediction with confidence.

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: The FEMM-era version — survey the bare magnet, reconcile with the simulation, THEN machine shims from the reconciled model. Same model-then-verify discipline as MacKenzie's aecd-1850.

there are many uncertainties in the exact determination of the constants of the equivalent circuit ... the calculated values ... serve well as a guide

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 82

Tabletop: A tabletop resonator IS the scale model — build the dee/stem mockup on the bench, measure f and Q before committing to vacuum hardware, and trust lumped calculations as guides not gospel. Berkeley used the same quarter-scale method on the 88-inch (ucrl-9435), which also confirms the Q-degradation-at-joints lesson (ornl-2648).

The circuit elements of the rf system were adjusted so that the first two higher modes would not be excited by an oscillator harmonic.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 5

Tabletop: DIRECT for a fixed-frequency machine: sweep the dee system to a few hundred MHz on a VNA, list the modes, and check none sits at 2f or 3f of the drive — if one does, detune it with a strap or stub BEFORE blaming the amplifier for instability. Same mode-vs-harmonic discipline as the msucp-9 and ornl-2648 lines.