1. Jiquan Guo, Haipeng Wang
CEBAF Pulsed Mode Operation for MEIC Proof of Principle Study Proposed for FY LDRD
Jiquan Guo, Haipeng Wang

2. MEIC Conceptual DesignIP
Future IP
Ion Source
Booster
MEIC
Collider
Rings
12 GeV CEBAF
Halls A, B, C
Electron Injector
Hall D
SRF Linac
e-SRF
i-SRF +
NCRF
Crab
Cooling
Layout is still evolving!
Stage I MEIC
CEBAF as full-energy e-/e+ injector
3-12 GeV e-/e+
8-100 GeV protons
<40 GeV/u ions
Stage II EIC
up to 20 GeV e-/e+
up to 250 GeV protons
up to 100 GeV/u ions

3. Bunch Filling Pattern in CEBAF
75.3ms, 10.5 revs in e-ring
Bunch train injected into the Figure-8 E-ring
Each bunch train 3.233ms
~2X e-ring trans damping time (12-700ms)
72.07ms
7.17µs, 1 rev in e-ring
24.23µs, 6 turns-0.967µs in CEBAF (4.2µs per turn)
51.07ms
~2X e-ring damping time
bunch train structure in the CEBAF North linac
0.967ms
Each bunch train 3.233µs
bunch train structure from the gun
75.3ms, 10.5 turns in e-ring

4. Requirement for CEBAF Pulsed beam with very low duty factor
Beam pulse width shorter than CEBAF rev time, no multi-pass BBU
Assume currently CEBAF can get ~1MW CW beam power from the cavities at 3-12 GeV, then we should be able to get ~5.5MW pulsed beam power in the proposed scheme.
Must maximize pulsed beam current to the RF power limit, especially at low energy end
𝐼 𝑖𝑛𝑗 ≈ 5.5(MW) 𝐸(GeV) (mA)
𝑇 𝑖𝑛𝑗 ≈2 𝜏 𝑑 𝐼 𝑟𝑖𝑛𝑔 (mA)𝐸(GeV) 5.5𝑀𝑊

5. Gradient Droop of Cavities
Cavity voltage with time varying beam loading and incident power, on resonance, no phase change
𝑉 𝑐 (t)= 𝑒 − 𝑡− 𝑡 0 𝑇 𝑓 𝑉 𝑐 𝑇 𝑓 𝑡 0 𝑡 𝑒 𝑡− 𝑡 0 𝑇 𝑓 𝑄 𝐿 𝑄 𝑒 𝑅 𝑄 𝑄 𝑒 𝑃 𝑖𝑛 (𝑡) − 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏 (𝑡)𝑐𝑜𝑠𝜙 𝑑𝑡
For periodical pulsed beam current 𝐼= 𝐼 𝑏 , 𝑛 𝑇 0 <𝑡<𝑛 𝑇 0 + 𝑇 𝑝 0, 𝑛 𝑇 0 + 𝑇 𝑝 <𝑡< 𝑛+1 𝑇 0
If we have a fixed incident power Pin:
𝑉 𝑐 𝑡 = 2 𝑄 𝐿 𝑄 𝑒 𝑃 𝑖𝑛 𝑅 𝑄 𝑄 𝑒 − 𝑒 𝑛 𝑇 0 + 𝑇 𝑝 − 𝑇 0 −𝑡 𝑇 𝑓 𝑉 𝐼 1− 𝑒 − 𝑇 𝑝 𝑇 𝑓 1− 𝑒 − 𝑇 0 𝑇 𝑓 − 𝑉 𝐼 (1− 𝑒 − 𝑇 𝑝 𝑇 𝑓 ),𝑛 𝑇 0 <𝑡<𝑛 𝑇 0 + 𝑇 𝑝 𝑉 𝐼 𝑒 𝑇 0 −𝑡 𝑇 𝑓 (𝑒 𝑇 𝑝 𝑇 𝑓 −1), 𝑛𝑇 0 + 𝑇 𝑝 <𝑡< 𝑛+1 𝑇 0
𝑉 𝐼 = 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏

6. Gradient Droop of Cavities
Example: A typical C100 cavity with max pulsed current (Ib=400 µA), pulse width Tp=10ms, period T0=20ms, Pin=2500W(CW)
Ib(A)
Vc(MV)
T(s)
Gradient droop with CW RF for a C100 cavity with typical Qe=3.2×107:
Vc(MV)
Ib(µA)
Tp (µs)
T0(ms)
ΔVc
13.7 (12GeV w/ margin)
400
10,000 20
59%
13.7 25 10
0.30%
5.0 (~4.8GeV operation)
0.81%
5.0
1000
2.05%
Will be worse in C50/C25 due to lower operation gradient
CEBAF arc momentum acceptance is ~0.2%

7. Use feed-forward to eliminate gradient droop
To eliminate gradient droop, we need to pulsate the klystron power and keep it synced with beam pulse This could be done with RF feed-forward + pulse-to-pulse feed-back. Klystron power and beam current need to be synced, with RF pulse slightly wider than the beam pulse (so the gradient droop won’t happen within the beam pulse). Pulse to pulse change in delay needs to be controlled to the order of 0.1µs or less For the above RF pulse structure, in the worst case (~3GeV), the finest beam time structure (~1µs pass to pass spacing) will cause the energy droop of ~0.2% in the first arc, but will average out in the higher energy arcs. Shorter pass to pass spacing (slightly larger storage ring) will also help. C100/R100 Qext needs to be lowered with stub-tuners for low gradient/high current operation
2 𝑄 𝐿 𝑄 𝑒 𝑅 𝑄 𝑄 𝑒 𝑃 𝑖𝑛 (𝑡) = 𝑉 𝑐 + 𝑅 𝑄 𝑄 𝐿 𝐼 𝑏 𝑡 𝑐𝑜𝑠𝜙
24.23µs, 6 turns-0.967µs in CEBAF (4.2µs per turn)
~1X e-ring damping time
RF pulse in a typical C100 cavity at 12.5MV 0.4mA synced with bunch train in the CEBAF North linac
0.967ms
Each bunch train 3.233µs
P=1.44kW
P=4.05kW
Flat Vc=12.5MV
~1X e-ring damping time
~1X e-ring damping time

8. Proof of Principle Experiments
Goal: confirm that CEBAF cavities can provide the current that meets MEIC electron storage ring injection requirement, providing a maximum of 1.5-2mA pulsed current without significant gradient droop
Stage 1: single cavity and single module operation
Utilize the injector spectrometer to monitor beam energy droop from quarter module and R-100, up to 25µs and 1.5-2mA beam pulse
Apply feed-forward in the injector R100 module and compare the voltage droop to the case w/o feed-forward
Stage 2: CEBAF multi-pass pulsed operation with C100s
Detune all the C20/C50
Apply feed-forward in C100 cryomodules, and try to get ~2MW (~5GeV 0.4mA) pulsed beam with ~4µs beam pulse width. Lower energy may be tested, but will be limited by the availability of stub tuners.