advanced beam manipulation, cooling, damping and stability 211
sible, the four-mirror optical cavities are more practical, 11
and are especially more impervious to disturbances.
Moreover, the four-mirror cavities can also be more suitably arranged when one needs to pass the electron beam
around the cavities, as shown in the third case presented in
Fig. 10.32.
There is an essential difference between the accumulation
of pulses of light and the accumulation of bunches of particles, as we will discuss momentarily.
10.4.2 Accumulation of charged particle bunches
Liouville ' s theorem: In the
vicinity of a particle, the particle density in phase space
is constant if the particle
moves in an external magnetic field or in a general field
in which the forces do not depend upon velocity.
S
T
FIGURE 10.33
Phase-space stacking.
The accumulation of bunches of charged particles (e.g., at injection) obeys Liouville’s theorem (see its full definition in the
margin).
The consequence of the theorem is the conservation of
emittance ε, i.e., the area p dq of the phase space beam portrait is constant (during accelerating, γε is constant).
Beam cooling methods (SR, electron, stochastic) do not
contradict Liouville’s theorem, as in these cases the cooling
forces acting on the particle depend on its velocity.
One important consequence of the theorem is that we cannot stack bunches of charged particles on top of each other in
the phase space. If we would like to accumulate them to increase the total intensity, we must inject the bunches into the
neighboring areas of the phase space (Fig. 10.33).
Phase-space stacking and accumulation of bunches during injection can be done in various ways. Fig. 10.34 shows
an example of transverse stacking.
FIGURE 10.34
Transverse phase-space stacking. Consecutive moments.
Longitudinal stacking is also possible, as illustrated in
Fig. 10.35. Fast-switching bending magnets or electrostatic
deflectors — kickers — are used to perform bunch stacking
during injection.
11 A. Variola et al., ThomX — Conceptual Design Report, LAL, 2010.
sible, the four-mirror optical cavities are more practical, 11
and are especially more impervious to disturbances.
Moreover, the four-mirror cavities can also be more suitably arranged when one needs to pass the electron beam
around the cavities, as shown in the third case presented in
Fig. 10.32.
There is an essential difference between the accumulation
of pulses of light and the accumulation of bunches of particles, as we will discuss momentarily.
10.4.2 Accumulation of charged particle bunches
Liouville ' s theorem: In the
vicinity of a particle, the particle density in phase space
is constant if the particle
moves in an external magnetic field or in a general field
in which the forces do not depend upon velocity.
S
T
FIGURE 10.33
Phase-space stacking.
The accumulation of bunches of charged particles (e.g., at injection) obeys Liouville’s theorem (see its full definition in the
margin).
The consequence of the theorem is the conservation of
emittance ε, i.e., the area p dq of the phase space beam portrait is constant (during accelerating, γε is constant).
Beam cooling methods (SR, electron, stochastic) do not
contradict Liouville’s theorem, as in these cases the cooling
forces acting on the particle depend on its velocity.
One important consequence of the theorem is that we cannot stack bunches of charged particles on top of each other in
the phase space. If we would like to accumulate them to increase the total intensity, we must inject the bunches into the
neighboring areas of the phase space (Fig. 10.33).
Phase-space stacking and accumulation of bunches during injection can be done in various ways. Fig. 10.34 shows
an example of transverse stacking.
FIGURE 10.34
Transverse phase-space stacking. Consecutive moments.
Longitudinal stacking is also possible, as illustrated in
Fig. 10.35. Fast-switching bending magnets or electrostatic
deflectors — kickers — are used to perform bunch stacking
during injection.
11 A. Variola et al., ThomX — Conceptual Design Report, LAL, 2010.