Proposed R&D topics Y. Derbenev for the design participants MEIC R&D meeting , August 27, 2015 R&D planning

Outline 2 I. R&D in frame of Base Line Magnetized ERL cooler Study of gear change impacts Choice of move magnets version II. Optimizing Linac and Rings designs 1. Small emittance e-collider ring 2. 100 MeV ion linac + two boosters injector III. Advanced studies 1. Magnetized ERL + CCR EC Electron storage ring-cooler /Y. Zhang/ Scanning Synchronization Circular Modes Optics for ion rings Matched Electron Cooling MEIC advanced beam physics study with a prototype of a front-end ion accelerator complex 2 2

Base line Synchronization 1. Move magnets is a baseline for today. Move electron magnets in arcs overall feels preferred (though doglegs and also matching CEBAF – collider ring look to be needed). Chicanes look disadvantageous (in my view) because of the design and alignment complexity. Gear vision 2. In my opinion, gear must be allowed - especially once N-physicists want to use it. In case, necessary stabilizing measures must be implemented. After all, gear seems not to present a dynamical problem. 3

Gear impacts an cure 4 Gear + Gaps effect vision Kink instability (which is an actual reduction of the gear dynamics, as to me) will be suppressed by Landau damping: collective dipole excitation of ion beam (as well as the electron one) happens in the non-linear field of the encountering beam with its fundamental non-linear tune spread. This tune spread exceeds the kink increment by one order of value for i-beam and two orders for e-beam. Similar picture should be actual in the longitudinal direction. Gear + Gaps effect vision Gear with gaps lead to stochastic incoherent dynamics in, again, non-linear beam-beam field. Potential heat mechanism for ion beam. However, my estimations show that it can be suppressed by electron cooling. I think we are able to develop an analytical study based on dynamics modeling with Vlasov + Liapunov + Landau stability equations. We should invite for cooperation Alexei Burov and Davresh Khasanyan. Of course, gear dynamics must be simulated in an adequate code way. 4

100 MeV ion linac + 2 boosters injector 100 MeV linac suggests about 100 M$ cost reduction (!) Design a (reasonably) shortest 3 GeV racetrack booster. Advantages: - reduction of Sp. Ch. by a factor about 2 (better emittance or higher current) two times shorter SC solenoid for proton spin Large Booster: E-ring to serve as large ion booster Design separate CF LB ring (400 M circumference) 6

Need small emittance e- ring Long PEP-II dipoles do not allow one to design the required electron emittance Possible improvement to investigate: - replace PEP II quads with SF quads (twice as strong) - ultimately, also replace PEPII dipoles with short ones (same field). Use SFQ or may be even SCQ. Are sextupoles absolutely needed in arcs? Place them in CCB ?/ gaining reduction of the 2nd order chromatic tune?/ 5

Scanning Synchronization idea We consider a scheme of the crab-crossing colliding beams with collision point moved periodically by a small scanning the beam directions in real time. For very most of the e-i bunch pairs, this scanning compensates for time delay of ion arrival at the nominal (central) Interaction Point (IP). The direction tilt of bunches is produced by RF deflecting resonators with amplitude and phase control of the RF voltage 𝑉 𝑠𝑠 . ions e- h In case that shift of the collision point (CP) is shared equally with the ion beam, the bypass parameters for each of two beams are reduced by a factor of 2, together with the similar reduction of the CP deviation. h ℎ 𝑚𝑎𝑥 =   8 𝜃 𝑐𝑟𝑜𝑠𝑠 = ± 𝛼 𝑚𝑎𝑥 𝐹 ; ⟶ (𝑉 𝑠𝑠 ) 𝑚𝑎𝑥 =𝛼 𝑚𝑎𝑥 𝐸 𝑉 𝑐𝑟𝑎𝑏 𝐸 = 𝜆 4𝜋𝐹 𝜃 𝑐𝑟𝑜𝑠𝑠 ; ⟶ (𝑉 𝑠𝑠 ) 𝑚𝑎𝑥 = 𝜋 2 𝑉 𝑐𝑟𝑎𝑏 Compare with 𝑉 𝑐𝑟𝑎𝑏 : tan 𝜑 0 = 𝑉 𝑠𝑠 𝑉 𝑐𝑟𝑎𝑏 Crabbing and scanning voltages can be combined in one cavity:

Adjustment of beam focusing at ScS A complete dynamic concept of ScS requires correction of focal distance of both beams in tact with the IP motion. This can be achieved in automatic regime by introduction of small constant sextupole magnets before the FFB of a proper strength. h ∆F F =− ∆(𝛻𝐵) 2𝛻𝐵 =− 𝐵 𝑠 ℎ 𝐵 𝑞 𝐴 ⟶ 𝐵 𝑠 𝐵 𝑞 =− ∆F 𝐹 𝐴 ℎ = 𝐴 𝐹 𝜃 𝑐𝑟 ions e- ∆F = ℎ 𝜃 𝑐𝑟𝑜𝑠𝑠 Here are the quadrupole and sextupole fields at conductors Here 𝐵 𝑞 and 𝐵 𝑠 are the quadrupole and sextupole fields value at conductors; 𝐴 is the aperture .

ScS cycles A cycle of the RF voltage control implies two tact: the collisions tact (CT) and the switching tact (ST). In CT, RF amplitude (including sign) changes linearly with time (according to the diagram of Fig. 2). During ST, the kicking RF voltage is supposed to be quickly returned to its initial amplitude and phase to start the next cycle. The cycle duration will be equal to the two inverse differences in the bunch repetition rates of two beams. Minimum duration of a cycle is equal 2 periods of beam revolution (14 mcs at 2.1. KM of circumference, i.e. 70 KHz rep. rate) ions e- ScS cycle rep. rate for 2.1 KM circuference is 70 KHz

Estimations of ScS parameters Electrons 𝜆=30 𝑐𝑚 ⟶ ∆𝐹=±3.75 𝑐𝑚; 𝜃 𝑐𝑟 =50 𝑚𝑟 ⟶ ℎ 𝑚𝑎𝑥 = ±2 mm 𝐹 𝑒 =4𝑚 ⟶ 𝛼 𝑒 =0.5 𝑚𝑟𝑎𝑑; 𝐴=3 𝑐𝑚 ⟶ 𝐵 𝑠 𝐵 𝑞 =0.15 𝐸 𝑒 = 10 GeV ⟶ Σ 𝑉 𝑠𝑠𝑒 =5 MV SRF power ≅10 𝐾𝑊𝑡 Protons 𝐹 𝑝 =7𝑚 ⟶ 𝛼 𝑝 =0.3 𝑚𝑟𝑎𝑑; 𝐵 𝑠 𝐵 𝑞 =0.085 𝐸 𝑝 = 100 GeV ⟶ Σ𝑉 𝑠𝑠𝑝 =30 MV SRF power ≅60 𝐾𝑊𝑡

Scanning Synchronization Electro-dynamic concept Modeling of energy transfer into the buffer cavity Conceptual scheme A novel method of energy recovery in the deflecting cavities, based on a fast transfer by beats of the stored energy in coupled high Q-factor cavities has been proposed and considered for use at ScS. Need a precise phase and amplitude control Need a superfast switch ! 7 G. Kazakevich 7.30.2015

Controlled Magnetron RF Source for ScS The magnetron transmitter providing a wideband phase and power control The proposed RF energy recovery method using efficient transmitters based on magnetrons frequency-locked by phase-modulated wide-band signal will be cost-effective and will allow a significant decrease of the RF power required for the deflecting cavities at the scanning synchronization. 8 G. Kazakevich 7.30.2015

Superfast Switch for ScS Photoconductive Semiconductor Switch (PCSS) for use in “MEIC Scanning Synchronization”. The PCSS switch was proposed as an advanced alternative to the PIN diode microwave switching circuit for control the energy transfer process in coupled resonators-cavities (see. G. Kazakevitch Conceptual scheme). The PCSS switch is a very fast photo-electrical  switch-device with a lot of potential applications including sub-nanosecond fast microwave switching. However, for use in the MEIC Scanning Synchronization the microwave circuit with embedded one or more optically controlled PCSS devices has to be designed, simulated and tested. Some PCSS models and semiconductor raw material dedicated for application in PCSS are available from the market (Kyma Technologies). V. Popov V. Popov 9

Superfast Switch for ScS (cont-d) List of questions which need to be answered: 1.       What type of semiconductor is preferred 2.       On/Off timing and ratio. 3.       Insertion loss 4.       Long term stability 5.       Operation inside of high strength microwave field. A possible microwave circuit and light pulse control system also must be designed and tested. V. Popov 10

Cooling Ring and Damping Ring Y.Zhang, V. Morozov, Jiquan Guo ion bunch electron bunch Cooling section solenoid Full energy injector E cooling ring Energy compensation ± ΔE E+ΔE ~100 MeV Energy compensation Damping ring ERL Multiple damping wigglers Red Interior Page Design 2

Enhancement of SR Damping With wigglers, with and without 100 MeV energy jump Proton energy GeV 8 30 60 100 250 Electron energy MeV 4.9 16.9 33.2 55 137 After jump 105 117 133 155 237 Relativistic γ 9.5 205 33.0 229 65.0 261 108 303 267 463 Energy loss/turn keV 0.01 6.3 0.16 7.8 0.63 10.1 1.7 13.7 10.6 32 Beam current A 1 SR power kW Damping time ms 165 7.7 47.5 6.9 24.1 6.0 14.6 5.2 5.9 3.4 (w/o wiggler) s 22423 538 70.4 15.5 1.0 Improving ratio 21.4 4.0 2.4 Energy spread 10-4 0.57 2.6 1.1 2.8 1.5 3.0 1.9 3.2 3.9 Red Interior Page Design 2

11 An investment: Circular Modes Optics of ion rings Advantages: Circular Modes Optics for ion rings A conventional background controversy: low emittance from linac – but large emittance in the rings due to the Laslett limit An investment: Circular Modes Optics of ion rings Advantages: 1) Overcoming the Sp. Ch. Limit (stacking, cooling, collider operation) 2) Potential to raise the e-cooling rate 3) Potential to overcome the SC limitation of luminosity Special tricks: - Round to flat ion beam transformation in IR - Matched Electron Cooling (matching i-beam with cooling solenoid) - 11

Circular Modes Optics for Low 4D Emittance Design beam transport around a ring with strong coupling (inserting the skew quads “on regular basis”), creating two circular modes (CM) of two naturally opposite helicities. Each of two individual CMs will look at a point of the orbit as a round (more generally, elliptical) turn by turn rotating pencil of particles with some phase advance. Similar to magnetized beam phase space structure, beam space charge can be “settled” just to one of two CMs, leaving other “empty” i.e. having a very low emittance. Such state can be achieved by initial filling one mode by injection from linac to the first, small booster (pre-booster) 12

Matched Electron Cooling Design circular modes ion ring optics Make ion focusing matched with the cooling section solenoid Betatron motion of ions is then represented as a superposition of the two independent circular modes of the two uncorrelated uncoupled canonical emittances, similar to the drift and cyclotron modes of an electron beam in a solenoid. Then cooling of the ion cyclotron mode is not limited by the ion space charge. It only can be limited by the IBS in ion beam. Drift mode associated with beam size in solenoid does not access an intrinsic friction effect. Cooling of the drift mode is attained by use of the energy dispersion of both beams introduced to the solenoid section. Cooling of this mode will be limited by the space charge. Ion optics organized in this way allows one to drastically diminish the space charge impact on the 4D emittance at beam stacking in a booster and cooling in a collider ring, thus enhancing the cooling rate. Equilibrium for cyclotron mode due to the IBS is estimated. We also will evaluate the gain in luminosity by means of a round to flat beam transformation around the Interaction Point.

Matched EC (cont-d) E-beam size in solenoid typically will be smaller than that of the ion beam Cooling can be optimized by scanning e-beam around the ion beam area.

Low energy ion front-end Test Facility (ITF) Polarized ion source, universal RFQ and DTL 10 MeV Small booster-synchrotron 200 MeV with DC EC -Coupled optics (circular modes) -Space charge with Circular Modes -Matched El. Cool. for low 4D emittance -Polarimetry tests -Study spin resonance, natural and RF (figure 8 ring) 13

Conclusion Goals of R&D beyond the baseline: ---Maintain conceptual superiority in the EIC capabilities, efficiency and operation cost compared with a RHIC-based EIC---