Considerations on the SuperB injection system

M. A. Preger

LNF/INFN

Injection requirements

• “Topping up” injection is mandatory to keep the average luminosity close to the maximum one

• Assuming an exponential decay, keeping currents > 90% of the maximum, with a luminosity variation within 20% below the maximum (10% loss in each beam current)

• Each bunch in the low energy ring must be refilled each 22 sec

• In order to fill both beams at this rate in the single bunch mode the injection repetition must be at least 160 Hz

DANE Linac• Scaling from DANE injection system, where

Linac pulse length is ≈10 ns, we can inject a train of 3÷4 bunches at each injection pulse, being the bunch separation in the SuperB rings 2.1 ns.

• The injection repetition in this case can drops below 50 Hz

• Partial recirculation of the beam to save on the Linac total length is possible

• Drawbacks of injecting >1 bunch:– slight loss in injection efficiency due the limited

longitudinal acceptance of the ring – necessity of a sufficiently flat Linac pulse to obtain a

constant current bunch pattern

Injection from Linac

• Required n. of particles to refill 10% current: 6.2x109 in LER possible with same Linac as in DANE

• In the DANE Linac:– Electron beam parameters: = 1

mmxmrad, energy spread of ±0.5% at 500 MeV. BUT: e- recent measurement at the end of the Linac on has given almost an order of magnitude smaller.

Injection from Linac

• Direct acceleration to 7 GeV into the Linac, yields a final due to adiabatic damping = 0.07 mmxmrad, corresponding to a beam size ≈ 6 times larger than the stored beam one.

• With an energy spread of 0.43% coming from prebunching within 15° in the injector section, the injected beam is half the size of the foreseen dynamic aperture.

Injection from Linac, Conclusions

• Direct acceleration in the Linac to 4 GeV would yield an emittance of 0.6 mm.mrad, corresponding to about 20 times the stored beam size, which is almost twice the dynamic aperture. This makes the use of a DR for e+ mandatory.

• e- can be safely injected into the HER, making simpler the design of a DR to be used only for positrons.

Injection scheme, summary

• Positrons accelerated to 4 GeV after conversion at 2 GeV, preaccelerated to 1 GeV, stored into a DR at 1 GeV and finally accelerated to 4 GeV.

• It is possible to inject 7 GeV e- directly from Linac

• This scheme fully exploits the total acceleration length of the Linac without any recirculation of the beam.

1 GeV Damping Ring• For 50 Hz injection of short bunch trains the damping

time should be a small fraction of 20 ms and RF frequency same as the main ring one.

• Therefore length of the DR must be a rational fraction of the main ring one, and also a multiple of the Linac bunch spacing

• Example: 40 m ring, transverse damping times ≈6.5 ms and synchrotron d. t. ≈3.3 ms. At 50 Hz, this is > 3 damping times for betatron oscillations and > 6 for the synchrotron ones.

• Assuming conversion at 2 GeV, the number of e+ in a 10 ns pulse from the Linac should be ≈5x1010, i.e. 8 times larger than the single bunch requirement for topping up injection, but injection of a small train of 3÷4 bunches at the same time will leave a safety factor of 2 on the single bunch charge.

• Equilibrium emittance in DR is 0.80 mmxmrad. With the beam extracted after 3 betatron damping times, extraction (e+) is 2% larger than the equilibrium one, about 3 times smaller than what can be obtained with direct acceleration in the Linac .

• Reacceleration in the Linac to 4 GeV yields an emittance of 0.20 mmxmrad, corresponding to a beam size 11 times larger than the stored beam one.

• The dynamic aperture is 12-13 times larger than the stored beam, so that injection from the damping ring is possible, but without any tolerance.

• A different design for the damping ring, to be used only for positrons, yielding at least a factor 2 smaller emittance is therefore recommended.

Energy spread

• The equilibrium energy spread in DR is 5.8x10-4

• Energy spread at injection into the main rings depends on the bunch length in the DR.

• With a RF at 476 MHz and 0.5 MV, the equilibrium bunch length is ≈6mm.

• With Linac at 3 GHz, this means that ±2s of the DR bunch occupies ≈85° on crest, which would give a very large energy spread at the end of the Linac.

• In order to come back to the 15° achievable with direct injection from the Linac, the bunch length must be reduced to ≈1 mm by means of a rather strong bunch compressing system.