The PS in the LEP injector chain - 50th anniversary of the CERN ...

The injection positron kicker was located in SS94 and the electron kicker in SS72. The kicker fall-time
was less than 250 ns, corresponding to less than one eighth of the PS circumference. The kick strength
(9 mrad) was strong enough that no slow injection bump was necessary. Single-turn injection was
achieved through the electron (positron) injection channel by means of a fast kicker magnet one eighth
of a betatron wavelength downstream of a pulsed septum magnet. There was no closed orbit bump in
the injection area so as to avoid aperture restrictions.
Chromaticity adjustments were performed with a small damping change at injection using the
PS auxiliary windings. A small energy damping partition number change of ΔJ e = −0.5 was obtained
through an unbalanced combined-function bending magnet field using the PS auxiliary winding
figure-of-eight loop. The ensuing tune change was cancelled by powering the focusing and defocusing
pole-face-winding coils. The sextupolar component of these coils modified the chromaticities and
made them positive in both planes, as required to avoid head–tail instabilities.
4 Emittance control of the PS lepton beams using a Robinson wiggler
In 1958, Robinson of the Cambridge electron accelerator (Massachusetts) proposed that a gradient
wiggler magnet be used to stabilize naturally unstable electron and positron beams in combinedfunction
machines. In 1986 such a method was applied in the PS so that it could serve as an
accelerator in the LEP injector chain. A prototype wiggler magnet was designed and constructed at
CERN. As predictions were confirmed by measurements carried out in the PS with electrons and in
the DCI (LAL, Orsay, France) with positrons to check the damping variations produced by this
wiggler, three wigglers were installed in the PS as it was part of the LEP injector chain [5].
A Robinson gradient wiggler magnet consists of an even number of combined dipole–
quadrupole magnet blocks of identical pole profile. The orientation of the pole profile is the same in
all four blocks with field and gradient of alternating polarity. The overall beam deflection is cancelled
by powering the half of the blocks with opposite polarities. To first-order this restricts the closed-orbit
perturbation and offsets the quadrupole focusing.
The damping of betatron and energy oscillations is proportional to the damping partition
numbers J x , J y , J e which can be expressed in terms of synchrotron radiation integrals I 2 and I 4 where D x
is the dispersion function, B y the magnetic field, ρ x the curvature radius, and k x =(B y ρ x ) -1 ∂B y /∂x the
normalized gradient
1
1 2
with (assuming a planar ring and wiggler sector magnets for simplicity)
12 .
An individual wiggler magnet adds a contribution ΔI 4 to I 4 and a small positive amount ΔI 2 to I 2
∆ 2
wiggler
4
Δ
wiggler
If the gradient wiggler is such that field and gradient are of opposite sign (i.e., B y ∂B y /dx < 0), its
contribution to ΔI 4 is negative and consequently ΔJ x is positive (though ΔI 2 > 0 slightly lessens the
positive change of J x ) and damping is increased in the horizontal plane. Hence the gradient wiggler
magnet increases the damping of radial betatron oscillations and decreases the damping of energy
oscillations (J e = 2 + I 4 /I 2 ).
Equilibrium transverse emittances and energy spread are reached when the mean quantum
excitation rates are equal to damping rates
.