FIGURE 5.10
RFQ structure.
80 unifying physics of accelerators, lasers and plasma
progress via 3D computer simulations of RF fields and beam
dynamics resulted in a widespread use of RFQs.
Most of the complicated linac designs discussed above
are applicable to hadrons, which (in practically achievable
accelerating gradients) become relativistic rather slowly, after a hundred or so meters of acceleration. Correspondingly,
the size and shape of accelerating cavities need to vary along
the hadron linac, so as to match their increasing velocity. For
electrons, which have already become highly relativistic after
a few tens of cm of acceleration, relatively simpler linac design is possible, in which cavities of the same size and shape
are regularly placed along the acceleration path.
5.1.5 Phase focusing
As we have seen in the previous section, the energy transferred to particles in a drift tube linac depends on the voltage
amplitude V
and phase Ψ 0 . We should note that a small
max
deviation of the nominal voltage V
would result in a parmax
ticle velocity that no longer matches the design velocity fixed
by the length of drift sections. In this case, the particles would
undergo a phase shift relative to the RF voltage and the synchronization of particle motion with respect to RF field will
be eventually lost.
The system can be made to self-adjust to such small deviations if we use Ψ 0 < π/2 so that the effective accelerating
voltage is V eff < V max , as shown in Fig.5.8. In this instance, if
a particle gains too much energy in the preceding stage and
is travelling faster than the ideal particle and arrives at the
next acceleration stage earlier, it will then feel the average RF
phase Ψ = Ψ 0 − ΔΨ and will be accelerated by the voltage
V
' = V
sin (Ψ 0 − ΔΨ) < V
sin Ψ 0
(5.3)
eff
max
max
which is below the ideal voltage. The particle will thus gain
less energy and will slow down and return to the nominal
velocity. The process will then repeat and the particles will
continuously oscillate about the nominal phase Ψ 0 , exhibiting the phenomena of phase focusing. If dissipation is present
in the system (such as SR damping), these oscillations would
eventually be forced to decay and the particles would gather
around the synchronous phase. A similar effect of bunching
can happen without damping, due to acceleration.
5.1.6 Synchrotron oscillations
The phase focusing of particles in accelerators manifests itself as the periodic longitudinal particle motion about the
nominal phase, and is called synchrotron oscillation.
In circular accelerators, as the ideal particle encounters
the RF voltage at exactly the nominal phase on each revolution, the RF frequency ω RF must be an integer multiple of the
RFQ structure.
80 unifying physics of accelerators, lasers and plasma
progress via 3D computer simulations of RF fields and beam
dynamics resulted in a widespread use of RFQs.
Most of the complicated linac designs discussed above
are applicable to hadrons, which (in practically achievable
accelerating gradients) become relativistic rather slowly, after a hundred or so meters of acceleration. Correspondingly,
the size and shape of accelerating cavities need to vary along
the hadron linac, so as to match their increasing velocity. For
electrons, which have already become highly relativistic after
a few tens of cm of acceleration, relatively simpler linac design is possible, in which cavities of the same size and shape
are regularly placed along the acceleration path.
5.1.5 Phase focusing
As we have seen in the previous section, the energy transferred to particles in a drift tube linac depends on the voltage
amplitude V
and phase Ψ 0 . We should note that a small
max
deviation of the nominal voltage V
would result in a parmax
ticle velocity that no longer matches the design velocity fixed
by the length of drift sections. In this case, the particles would
undergo a phase shift relative to the RF voltage and the synchronization of particle motion with respect to RF field will
be eventually lost.
The system can be made to self-adjust to such small deviations if we use Ψ 0 < π/2 so that the effective accelerating
voltage is V eff < V max , as shown in Fig.5.8. In this instance, if
a particle gains too much energy in the preceding stage and
is travelling faster than the ideal particle and arrives at the
next acceleration stage earlier, it will then feel the average RF
phase Ψ = Ψ 0 − ΔΨ and will be accelerated by the voltage
V
' = V
sin (Ψ 0 − ΔΨ) < V
sin Ψ 0
(5.3)
eff
max
max
which is below the ideal voltage. The particle will thus gain
less energy and will slow down and return to the nominal
velocity. The process will then repeat and the particles will
continuously oscillate about the nominal phase Ψ 0 , exhibiting the phenomena of phase focusing. If dissipation is present
in the system (such as SR damping), these oscillations would
eventually be forced to decay and the particles would gather
around the synchronous phase. A similar effect of bunching
can happen without damping, due to acceleration.
5.1.6 Synchrotron oscillations
The phase focusing of particles in accelerators manifests itself as the periodic longitudinal particle motion about the
nominal phase, and is called synchrotron oscillation.
In circular accelerators, as the ideal particle encounters
the RF voltage at exactly the nominal phase on each revolution, the RF frequency ω RF must be an integer multiple of the