What has to be redone for any change is the design-point pair of magnetic field and radius, the first-orbit clearance, the tank (coil plus dee capacitance), and the vacuum budget (the pressure the spiral needs, set against the gas the source admits and the pumps remove). What has to be measured again is the magnetic field at the centre against coil current and the dee capacitance, the capacitance between the dee and the grounded chamber around it; a field map is for when the beam’s behaviour calls for one (Do I really need to map my magnet's field accurately? Is one reading in the middle enough, and which value goes into the frequency and energy calculations?).
If it does not work. Change the magnet and you change the field, which moves the RF
frequency and the energy ceiling together; the Rutgers 12-inch needed a new tank coil just to run
at half frequency for deuterons (Koeth (2017), p. 1). Change the magnet gap and you change the focusing profile (the field’s fall-off with radius), the voltage the gap can hold, and the clearance the first turn needs around the source. Change the
chamber or the dee and you change the capacitance the tank resonates against. One college build
skipped measuring it and tuned by trial and error; Houghton measured 79 pF and designed from it
(Cressman (2006), p. 18). Change the dee voltage and you change the turn count, which changes the vacuum the
spiral needs and whether the first orbit clears the source (Prechtl & Wolf (2020), p. 54, Prechtl & Wolf (2020), p. 42-43). Change the ion
source and you change the gas load the pumps must carry (vacuum page). Almost nothing is a free
substitution. ORNL’s verdict on a machine built fast from adapted parts: it
ended up unshieldable, with a marginal field, a capped dee voltage and a gap half of what was
needed, and none of it could readily be corrected (Howard (ed.), p. 20).
Many projects start with a surplus magnet, and it can work. The Rutgers 9-inch ran on a Varian NMR magnet turned on its side, Houghton on a commercial
laboratory electromagnet, COLUMBUS on a donated Bruker magnet (census). It is no guarantee of success:
the Knox College build was designed around the chemistry department’s 2 T NMR magnet and never
documented a beam, though the record does not say why (census). The record supports
the method: design from the magnet’s measured field-versus-gap curve and usable radius (Dewan (2007), p. 7-8),
and check that the frequency and RF that fall out of that field are ones the builder can actually
produce. A 2 T field, with the proton frequency rising in step with the field, means a 30 MHz proton RF
system holding kilovolts, on a small usable radius.
To understand it. The precedent for copying is institutional. When the University of Washington built its
60-inch, it obtained the complete Berkeley drawings, followed them closely on the magnet, reserved
original effort for the places the plans were silent, and had the machine assembled and ready to
test in three years (The University of Washington 60-Inch Cyclotron: Progress and Status…, p. 6). At amateur scale the finished census machines are documented in
build logs and theses. A design point taken from COLUMBUS or Rutgers is one known to work
(choosing-your-machine page). The COLUMBUS authors, though, could
draw only partly on the amateur machines before them because “the boundary conditions were too
different” (Prechtl & Wolf (2020), p. 8). A copy is a copy of a configuration, not of a parts list.
On scaling: magnetostatics, the physics of steady magnetic fields, has no intrinsic length scale, so
a geometrically scaled magnet, every dimension multiplied by the same factor, run at
the same field reproduces the same field distribution, the same pattern of field across the gap
(Wakerling & Guthrie (eds.), p. 25). The field distribution is the
one thing that scales cleanly, and it sets a trap. The cyclotron frequency depends on the field, not on the size
of the machine, so a half-size machine at the same field still needs the same RF frequency. A
geometrically scaled resonator, though, has a natural frequency that doubles when its size halves,
because the inductance and the capacitance that set it both shrink with its dimensions
(MacKenzie (1947), p. 6). The RF
circuit therefore has to be redesigned to the field, not shrunk with the iron. The energy, meanwhile, scales
as (Br)², so the half-size machine reaches a quarter of the energy at the same field. When the Rutgers group moved from its working 9-inch
prototype to the 12-inch magnet, the beam did not come with it: fractions of a nanoampere
against the prototype’s ten, and a diagnosis that ran through the pole tips to the ion source
before the machine recovered (Koeth (2006), p. 1). It is an
illustration of redesign and recommissioning, not a controlled experiment that isolates scale as
the cause; nothing carried over automatically.