MEIC Electron Cooling Simulation

He Zhang03/18/2014, EIC 14 Newport News, VA

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Outline

• Introduction • MEIC Multi-phased Cooling Scheme• MEIC Cooling Simulation Studies

• Case 1: Nominal Design (Three-Stage Cooling)• Case 2: No Electron Cooling in the Collider Ring• Case 3: With “Weak cooling” in the collider ring

• Conclusion and discussions

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Introduction• The MEIC conceptual design aims for reaching ultra high luminosity

up to 1034 cm-2s-1 per interaction point

• The MEIC luminosity concept is based on high repetition rate crab- crossing colliding beams.

• This design concept relies on strong cooling of protons & ions • Achieving small transverse emittance (small spot size at IP)• Achieving short bunch (with strong SRF)• Enabling ultra strong final focusing (low β*) and crab crossing• Suppressing IBS, expanding high luminosity lifetime

• MEIC design adopts traditional electron cooling

• MEIC design adopts a multi-phase cooling scheme for high cooling efficiency

• We use computer simulations to validity the cooling design concept and beam parameters

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MEIC Three-Step Cooling Scheme• Multi-phased scheme takes advantages of high electron cooling

efficiency at low energy and/or small 6D emittance

Step 1: Low energy DC cooling at the pre-boosterStep 2: Bunched cooling at the ion injection energy (25 GeV) of the

collider ringStep 3: Bunched cooling at the top ion energy (100 GeV) of the

collider ring

MEIC ion complex

Yaroslav DerbenevTalk on Tuesday

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DC and ERL-Circulator Cooler for MEIC

ion bunch

electron bunch

circulator ring

Cooling section

solenoid

Fast kickerFast kicker

SRF Linac dumpinjector

MEIC needs two electron coolers• DC cooler (within state-of-art, a 2 MeV cooler is in commissioning at COSY)• ERL circulator cooler need significant R&D

High energy cooler – beyond state-of-the-art – there are significant challenges

• Cooling by a bunched electron beam• Making and transport of high current/intensity magnetized electron beam

Present design conceptERL + circulator ring

To meet following challenges • High RF power (up to 81 MW) • High current ERL (up to 1.5 A)• High current source (short lifetime)

Yaroslav DerbenevTalk on Tuesday

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MEIC Cooling Simulation

Assumptions for simulation• Ion beam has Gaussian distribution.• Electron beam is magnetized.• Electron beam has uniform distribution in the DC cooler (pre-

booster) and Gaussian distribution in the ERL circulator cooler (Collider ring).

• The shape and distribution of electron beam does NOT change during cooling.

• Misalignment is not considered.• Cooler is modeled as thin lens.• BETACOOL is used for the simulation.

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Simulation ParametersKey parameters for MEIC three-step cooling scheme

Pre-Booster Collider Ring Collider RingProton Energy GeV 3 25 60/100 Proton Number 2.52×1012 1.26×1013 4.16×109/bunchProton Bunch Length cm Coasting Coasting 1

Cooler Type DC ERL circulator ERL circulatorMagnetic Field in Cooler T 1 2 2Cooler Length m 10 2×30 2×30Electron Beam Current A 3 1.5 1.5

Electron Bunch Length cm 1 1

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Step 1: Cooling in Pre-Booster (3 GeV)

IBS ECOOL IBS+ECOOLRH 1/s 0.0009 -0.0073 -0.0064

RV 1/s 0.0002 -0.0072 -0.0070

RL 1/s 0.0003 -0.0128 -0.0125

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Step 2: Cooling in Collider Ring (25 GeV)

IBS ECOOL IBS+ECOOLRH 1/s 0.0005 -0.0169 -0.0164

RV 1/s 3.47×10-5 -0.0118 -0.0118

RL 1/s 0.0009 -0.0242 -0.0233

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Step 3: Cooling in Collider Ring (60 GeV)

IBS no coupling

IBS ECOOL IBS+ECOOL

RH 1/s 0.0214 0.0204 -0.0221 -0.0017

RV 1/s 0.0002 0.0015 -0.0079 -0.0064

RL 1/s 0.0069 0.0069 -0.0086 -0.0016

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Step 3: Cooling in Collider Ring (100 GeV)

IBS no coupling

IBS ECOOL IBS+ECOOL

RH 1/s 0.0156 0.0078 -0.0087 -0.0009

RV 1/s 4.99×10-5 0.0094 -0.0107 -0.0013

RL 1/s 0.0035 0.0035 -0.0043 -0.0007

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No Cooling in The Collider Ring: Emittance Growth and Luminosity Decay Due to IBS

• The DC cooling in pre-booster (3 GeV) provides an initial emittance reduction to 0.8 and 0.55 mm mrad

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No Cooling in The Collider Ring: Emittance Growth and Luminosity Decay Due to IBS

• The DC cooling in pre-booster (3 GeV) provides an initial emittance reduction to 0.8 and 0.55 mm mrad

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No Cooling in The Collider Ring: Emittance Growth and Luminosity Decay Due to IBS

• The DC cooling in pre-booster (3 GeV) provides an initial emittance reduction to 0.8 and 0.55 mm mrad

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No Cooling in The Collider Ring: Emittance Growth and Luminosity Decay Due to IBS

• The DC cooling in pre-booster (3 GeV) provides an initial emittance reduction to 0.8 and 0.55 mm mrad

Cooling at High Energy w/ Existing Technologies

• Only for heavy ions• Bandwidth: 4~9 GHz• Lead ions: 5.1x107 per bunch• Bunch length: 2 cm effective ions in the ring: 1.37x1012 • Cooling time: ~ 14 min

ion bunch

electron bunch

circulator ring

Cooling section

solenoid

Fast kickerFast kicker

SRF Linac dumpinjector

“Weak” ERL Cooler Bunched Stochastic Cooling

RHIC

• No circulating ring (no fast kicker)• Electron current: ~ 100 mA• Electron bunch charge: 0.133 nC• Electron beam power: 2.75 to 5.5 MW• Needs ERL

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With “Weak” Cooling in Collider Ring (25 GeV)

IBS ECOOL IBS+ECOOLRH 1/s 0.0004 -0.0048 -0.0044

RV 1/s 3.47×10-5 -0.0034 -0.0033

RL 1/s 0.0009 -0.0069 -0.0060

• At 25 GeV, a “weak” cooling by 330 mA electron beam is strong enough to cool the coasting proton beam.

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With “Weak” Cooling in Collider Ring (60 GeV)• At 60 GeV, reduce proton charge number to 3×109/bunch to reduce IBS• Luminosity is about 3×1033cm-2s-1

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With “Weak” Cooling in Collider Ring (100 GeV)• At 100 GeV, reduce proton charge number to 3×109/bunch to reduce IBS• Luminosity is about

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Luminosity of Strong Cooling, Weak Cooling and No Cooling in Collider Ring

• 60 GeV • 100 GeV

• Nominal design: 6.5×1033cm-2s-1

• Weak cooling: 3×1033cm-2s-1

• No cooling: above 2×1033cm-2s-1

in two hours.

• Nominal design: 5.4×1033cm-2s-1

• Weak cooling: 1.5×1033cm-2s-1

• No cooling: above 1.6×1033cm-2s-1

in two hours.

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ConclusionsUnder ideal condition

• In Pre-booster, KEp=3GeV, ε reduced from 1.75 μm to 0.8/0.55 μm. (Similar with the DC cooler in COSY)

• In collider ring, KEp=25GeV, ERL circulator cooler, ε reduced to 0.3/0.25 μm.

• In collider ring, KEp=60~100GeV, ERL circulator cooler, maintain or further reduce ε.

• Design parameters of MEIC cooling system is achievable.

• Even without the cooling in the collider ring, the luminosity is above 1033 cm-2s-1 in two hours

• A weak cooling (state of art) in the collider ring can keep the luminosity above 1033 cm-2s-1

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Future Works

• Gaussian distribution of the ion beam is assumed during the cooling process, which is not necessarily true.

• Analytical formulas are used to calculate the friction force, and their accuracy in MEIC parameter range needs to be checked.

• How electron bunch distribution changes during the cooling process and the effects on cooling due to the changes need to be studied, since they are repeatedly used.

• More accurate models may need to be developed and applied.

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