Scaling of High-Energy e+e - Ring Colliders

1. Scaling of High-Energy e+e- Ring Colliders K. Yokoya 2012.3.15 Accelerator Seminar, KEK

2. Proposed Ring Colliders • Recently several authors suggested possibilities of e+e- ring colliders for Ecm>200GeV. • T.Sen, J.Norem, Phys.Rev.ST-AB 5(2002)031001C=233km tunnel for VLHC • A.Blondel and F.Zimmermann, CERN-OPEN-2011-047, Jan.2012 (Version 2.9). arXiv:1112.2518LEP3, DLEP • K.Oide, "SuperTRISTAN: A possibility of ring collider for Higgs factory", KEK meeting on 13 Feb 2012.SuperTRISTAN • G.Lyons, arXiv:1112.1105 [physics.acc-ph], Feb.2012.PhD thesis. Nanobeam version of A) • D.Summers,et.al. “Rapid Recycling Magnets - Tests & Simulations”, Muon Accelerator Program 2012 Winter Meeting, 4-8 Mar.2012. SLAC.Small ring version of D)

3. Reference Parameters

4. Common Features • For reducing synchrotron radiation • Large circumference • small number of bunches compared with BFactories • Bunch collision frequency ranges 5kHz to ~150kHz compared with 13kHz in ILC • Luminosity similar to ILC •  Luminosity by one bunch collision comparable to ILC •  Beamstrahlung similar to ILC

5. Beamstrahlung for Proposed Parameter Sets

6. Beamstrahlung • The average energy loss and the number of photons per electron for the head-on collision with beam energy E=gmc2, bunch charge eN, rmsbunch length sz, beam size sx, sy, are given by integration length BB Field • For flat beams, sx+sy~sx

7. Interaction Length • In the case of head-on collision, the orbit length in the on-coming beam is effecttively min(sz, by) • In the nanobeam scheme, chooseby<<sz. The interaction lengthis ~min(by, sx/f)(f= half crossing angle) • Combining these, define • As crude approximation, Leff can be used instead of sz in the formulas of Luminosity, tune-shift, energy loss, number of photons. • Note: better to eliminate by for beamstrahlung because the beamstrahlung is insensitive to the vertical beam size. But OK because we consider here only the case of by close to either one the of others. sx/f 2f sz

8. Relevant Formulas

9. Beamstrahlung Limit • If you raise the beam energy under tuneshift limit with fixed beam structure, the power limit of synchrotron radiation is soon reached. • If the upper limit of power is set high, beamstrahlung limit is reached soon or later. • Beamstrahlung limitis very much different between Ring collidersand Linear colliders • In the case of Linear colliders, the limit comes basically from physics requirements. (Very high beamstrahlung, e.g., >20%, may also be a problem of accelerator: to safely lead the beam to the dump.) • In the case of Ring colliders, the beam after beamstrahlung must circulate safely over the ring. The energy loss by one collision dBS (energy spreadis comparable or larger – discuss later) will accumulate over the radiation damping time. The equilibrium energy spread will be aboutSqrt(number of turns in damping time)x dBSwhich is order of percent even if dBS=0.1%. Very large momentum aperture is needed.

10. Beamstrahlung Limit での Luminosity • Once the beamstrahlung limitis reached, the luminosity above this energy goes down as 1/E4（Or 1/E4.5 if geometric emittance is fixed) • If the bunch charge is reduced to 1/n, dBS reduces by1/n2but the luminosityis also reduced by 1/n2. To restore the luminosity the number of bunches must be increased by n2times, hence the required power increases by n2 x 1/n = n .

11. Increase of dynamic aperture by a significant factor is unrealistic • For given luminosity and power consumption the only cures are • Huge ring (like 233km of VLCC) • Extremely small vertical emittance (like <1pm of CW250 and Summers)

12. Energy Spread • What really matters in ring colliders is not the average energy loss dBSbut theenergy spread sBS • The former is anyway compensated by the RF system • The energy spread due to the beamstrahlung is discussed in K. Yokoya, NIM A251 (1986) 1-16 for round Gaussian beam and elliptic cylinder beam. • There are two mechanisms of energy spread • Orbit in the on-coming bunch is different from particle to particle • Stochastic spread even along the same orbit • It was shown the latter is dominant unless ng (number of photons) is very large, e.g., for round Gaussian beams almost no correlation between successive collisions • If the typical photon energy is w , then the average energy loss is • dBS~ng w • and the spread due to the stochastic process is • sBS~ (ng)1/2 w • Hence , • sBS~dBS / (ng)1/2

13. Energy Spread(continued) • According to the simulations for the above parameter sets (and others),sBS~ 2.4dBS / (ng)1/2 • For not totally unrealistic parameter sets, ng is about 1 or less. • Hence sBS is significantly larger than dBS • The equilibrium energy spread is the square sum of synchrotron radiation and beamstrahlung. The latter is approximately

14. Luminosity Scaling with Given se

15. Conclusions • The luminosity scaling of ring colliders at beamstahlung limit is established. • The ring colliders (in particular for Ecm=400 and 500GeV) are scientifically impossible because of the energy spread due to the beamstrahlung, under the constraints that the luminosity and power consumption are comparable to those of ILC. The only way to solve is • Huge ring • Extremely small vertical emittance • The machine for Ecm=240GeV is at the border of feasibility. It is not a trivial machine. It requires serious studies of lattice design with very large momentum aperture or very small vertical emittance.