Guided exercises · 4 of 6
Where the Ions Are Born
Goal. How much of a source's output becomes beam is mostly decided in the first millimetres of an ion's life: capture into a stable orbit depends on where ions start. Making more ions scales the result and fixes nothing.
Who it is for. Readers of How a Cyclotron Works; no arithmetic. About fifteen minutes.
Predict first
Two questions. If the source makes twice as many ions, does the collector see twice the beam? And if the source moves one millimetre up or down, out of the machine's midplane, what changes: nothing, a little, or a lot? Most people answer yes to the first and "a little" to the second. Write both answers down before you open the laboratory.
There is no formula to work here; the prediction is qualitative. The thing to hold onto is where the source sits: at the centre, where the orbits are smallest and the electrodes nearest, so a millimetre there is a far larger share of the room an ion has than a millimetre at the collector.
The shape to expect
Open the laboratory
The link opens the laboratory at its working reference with the source controls shown. The primary move is the vertical source offset (under "More controls": the source offset's z value): move the source one millimetre up, then one millimetre down. The control experiment is source strength: back at zero offset, double the emission. Tick the box that draws lost paths to see where the early orbits end. The readouts to watch are the collected current and, in the Full workspace, the accounting panel's collected fraction.
Open the Virtual Cyclotron Laboratory (hosted; illustrative, not a calibrated replica)
What you should see
A millimetre of vertical offset cuts the collected current by a large factor while the emission readout stays where it was; the drawn lost paths end within the first turns — near the centre, long before the collector. Doubling the emission doubles the current and leaves the collected fraction where it was: the machine captured the same share of twice as many ions. That clean scaling is the laboratory's, whose simulated ions do not interact with one another; a real source turned up also changes its gas load, its plasma and, at useful currents, the beam's own space charge. One change moved the machine's output by a few percent of emission; the other scaled everything and fixed nothing.
If you see something different
The laboratory's two machines respond to different offset directions, because their source geometries differ: on the prototype the vertical move is the one that bites, and on the resolved-field machine a sideways offset acts as well. If a move does nothing, try the other axis. Every reading comes from an ensemble of simulated ions and scatters by a few percent from run to run; the scatter is the ensemble's own, so compare fractions across runs. The laboratory is an illustrative machine shaped like the reference machine, not a calibrated replica of any real machine; how much a millimetre costs a real source depends on that source's geometry.
The physics, cited
Where an ion starts and how hard it is pushed together decide whether its orbits are centred. A 1950s cyclotron report records that "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" (dg-810): a geometric constraint on the dee voltage, the rule notes, rather than one set by the RF power available.
In the central region the gap's electric field can defocus, and one machine's report puts the resulting loss on the dee surfaces above and below the midplane: "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" (dg-359). That is one machine's figure. The laboratory's vertical offset starts the ion nearer those surfaces.
The first orbit has to miss the source it came from. On one teaching cyclotron, protons were "clear of the source from 200 V" of dee amplitude on the first turn, and H₂⁺ ions from 400 V (dg-1387): below that, the ion's first turn is smaller than the source housing.
Timing selects too. With an internal source, "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)" degrees (dg-576): roughly 110 degrees of the 360 the RF cycle offers. For a source emitting evenly through the cycle, most of what it emits is then never a candidate for acceleration; the rule's note calls this a ceiling for a typical central region, not a measured capture efficiency, and the window itself depends on the geometry.
Background: the source lives or dies in the first half-turn in the ion-sources page.
Closing question
In one sentence: what did you change, what happened, and why? There is no form; the sentence is for you.