By D. A. Edwards
The 1st part bargains with the movement of a unmarried particle below the impression of digital and magnetic fields. the elemental language of linear and round accelerators is built. the main of part balance is brought besides part oscillations in linear accelerators and synchrotrons. offers a therapy of betatron oscillations by way of an day trip into nonlinear dynamics and its software to accelerators. the second one part discusses depth based results, really house cost and coherent instabilities. contains tables of parameters for a range of accelerators that are utilized in the varied difficulties supplied on the finish of every bankruptcy.
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Additional resources for An Introduction to the Physics of High Energy Accelerators
So we need to retain the feature of constant orbit radius while avoiding the monotonic field increase of the betatron; that is, we turn to oscillating fields. 4 were energized only during the time when the particles pass through it. 6 would provide an electric field synchronized with particle passage, and the oscillatory character of the waveform indicates that the magnetic fields associated with charging the capacitor are also oscillatory in character. One more step is necessary in order to complete our rudimentary picture of a high energy accelerator.
20. Contours of particle motion in longitudinal phase space obtained by solving the differential equations of motion. The curves shown are for q > 0 and for the coses (a) 4Js = w , (b) 4, = 57r / 6, and (c) 4' = 2 0 / 3. -41 PHASE STABILITY From this expression, we see that the correct choice for the synchronous phase depends upon the value of 7 as anticipated by our earlier discussion. For < 0, that is, y < y,, the motion is stable for cos 4, > 0. However, for 77 > 0 (y > y,), the synchronous phase must be such that cos 4, < 0.
By pressurization of the tank containing the accelerator, potential differences up to about 15 MV can be achieved. In the tandem Van de Graaff, in effect the voltage is doubled. In the tandem, the ion source is located at ground potential and emits a beam of negative ions-for instance, H-. At the high voltage terminal, the beam is passed through a foil which strips the electrons from the ions, and the protons continue to be accelerated, arriving at gound potential with twice the energy that would be associated with the electrostatic potential difference.