MEIC low rep-rate operation and path length Jiquan Guo 2/19/2015

Luminosity and collision rate 𝐿≈ 𝑓 𝑐 𝑁 𝑒 𝑁 𝑖 4𝜋 𝜎 𝑥 ∗ 𝜎 𝑦 ∗ = 1 𝑞 𝑒 𝐼 𝑒 𝑁 𝑖 4𝜋 𝜎 𝑥 ∗ 𝜎 𝑦 ∗ = 1 𝑞 𝑒 2 𝐼 𝑒 𝐼 𝑖 𝑓 𝑐 4𝜋 𝜎 𝑥 ∗ 𝜎 𝑦 ∗ Luminosity can be either limited by charge per bunch (mainly due to beam-beam effect) or total beam current (mainly due to SR power/HOM impedance in e-ring and space charge effect at injection energy in i-ring). To optimize luminosity, ideally we should choose a rep-rate (and emmitance) that let both charge per bunch and total beam current reach the limit. The optimal rep-rate depends on beam energy and other factors; higher beam energy prefers lower rep-rate, due to lower beam current from stronger SR, and weaker beam-beam effect from more rigid beam and larger e-ring emmitance. Currently, even at 4×30GeV, we still have room for beam-beam tune shift. Collision rep-rate must be a fraction of main RF frequency and a multiple of beam revolution frequency. An ideal ring harmonic number should provide as many factorization as possible. One good harmonic number for 476.3MHz base frequency is 3360 (=3*5*7*32)

Sync the electron and ion beam To sync electron beam with the proton/ion beam with different energy/velocity, we need to adjust the path length of one storage ring. We can also change the harmonic number of that storage ring, so the max change in path length is limited to 1 main RF wavelength. If we change the path length of the e-ring, main RF frequency must be adjusted, which may cause challenge toward syncing with the injector as well as cavity design; changing the i-ring path length may be more challenging due to its higher energy. Currently we assume that i-ring path length will be adjusted, and harmonic number is variable.

Injection and bunching Electron ring: Adjust injector gun trigger rate to achieve desired fill pattern The gun already has a base trigger rate at 1/7 of ring RF frequency. Need to lower the gun trigger rate further if other collision rate is desired. Even collision rate like 1/2 or 1/5 of ring RF frequency will result in higher charge per bunch in the injector, which may incur challenges for the gun R&D and RF transient effect, especially at low energy where injection time is already long. Ion ring Use different RF bunching frequencies after injection. Bunching voltage requirement won’t be prohibitive. A multi frequency bunching cavity will be helpful

possible collision rate as a fraction of 476MHz Option 1 for 476.3MHz system e-ring harmonic number: 3360 Circumference(m) 2114.768 ion ring min 2114.074 Max 2114.704 possible collision rate as a fraction of 476MHz Harmonic number Energy(GeV/u) γ β max 3360 36.617 120.000 39.037 127.932 0.99967 0.99997 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/10, 1/12, 1/14, 1/15, 1/16, 1/20, 1/21, 1/24, 1/28, 1/30, 1/32, 1/35, 1/40, 1/42, etc 3361 26.522 36.622 28.275 39.042 0.99937 NA 3362 21.838 26.526 23.282 28.279 0.99908 1/2, 3363 18.996 21.842 20.251 23.285 0.99878 1/3, 3364 17.037 18.998 18.163 20.254 0.99848 1/2,1/4 3365 15.582 17.039 16.612 18.165 0.99819 1/5, 3366 14.447 15.584 15.401 16.614 0.99789 1/3, 1/2, 1/6

Option 1 after 952.6MHz upgrade e-ring harmonic number: 6720 Circumference(m) 2114.768 ion ring min 2114.074 Max 2114.704 Harmonic number Energy(GeV/u) γ β possible reprate as a fraction of 952MHz max 36.617 120.000 39.037 127.932 0.99967 0.99997 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/10, 1/12, 1/14, 1/15, 1/16, 1/20, 1/21, 1/24, 1/28, 1/30, 1/32, 1/35, 1/40, 1/42, 1/48, 1/50, etc 6722 30.378 36.622 32.386 39.042 0.99952 1/2, 6722, 6723 26.524 30.380 28.277 32.388 0.99937 1/2, 1/3 6723, 6724 23.843 26.526 25.419 28.279 0.99923 1/2, 1/3, 1/4 6724, 6725 21.840 23.845 23.284 25.421 0.99908 1/2, 1/4, 1/5 6725, 6726 20.270 21.842 21.610 23.285 0.99893 1/2, 1/3, 1/5, 1/6 6726, 6727 18.997 20.272 20.253 21.612 0.99878 1/2, 1/3, 1/6, 1/7 6727, 6728 17.937 18.998 19.123 20.254 0.99863 1/2, 1/4, 1/7, 1/8 6728, 6729 17.038 17.939 18.164 19.124 0.99848 1/2, 1/3, 1/4, 1/8 6729, 6730 16.262 17.039 17.337 18.165 0.99834 1/2, 1/3, 1/5, 1/10 6730 15.583 16.263 16.613 17.338 0.99819 1/2, 1/5, 1/10 6732 14.447 15.584 15.401 16.614 0.99789 1/2, 1/3, 1/4, 1/6, 1/12

possible reprate as a fraction of 476MHz Option 2 for 476.3MHz system e-ring harmonic number: 3360 Circumference 2114.768m f 476.318 ion ring Harmonic number Energy(GeV/u) γ β Circumference(m) possible reprate as a fraction of 476MHz min max 3350 36.567 120.000 38.984 127.932 0.99967 0.99997 2107.78 2108.41 1/2,1/5,1/10 3351 26.485 36.572 28.235 38.990 0.99937 1/3, 3352 21.807 26.488 23.248 28.239 0.99907 1/2, 1/4, 1/8 3353 18.968 21.810 20.222 23.252 0.99878 1/7, 3354 17.012 18.971 18.136 20.225 0.99848 1/3, 1/2, 1/6 3355 15.559 17.014 16.588 18.139 0.99818 1/5, 3356 14.425 15.561 15.379 16.590 0.99788 1/2,1/4

possible reprate as a fraction of 476MHz Option 3 for 476.3MHz system e-ring harmonic number: 3360 Circumference 2114.768m ion ring Circumference(m) min 2109.669 Max 2110.298 Harmonic number Energy(GeV/u) γ β possible reprate as a fraction of 476MHz max 3353 36.582 120.000 39.000 127.932 0.99967 0.99997 1/7, 3354 26.496 36.587 28.247 39.005 0.99937 1/2, 1/3, 1/6 3355 21.817 26.500 23.259 28.251 0.99908 1/5, 3356 18.976 21.820 20.231 23.262 0.99878 1/2,1/4 3357 17.019 18.979 18.144 20.234 0.99848 1/3, 3358 15.566 17.022 16.595 18.147 0.99818 1/2, 3359 14.432 15.568 15.386 16.597 0.99789

Summary Low collision rate can help to improve luminosity at certain energies of MEIC. It can be achieved by change the injection pattern in e-ring and add bunching system in i-ring Several harmonic number options are available to make the low collision rate possible for different energy, assuming harmonic number of ion ring will change to accommodate the ion velocity change and limit the path length change to 0.63m.