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Homework Monday, June 15 th 2015

Calculate bunch spacing, revolution and repetition frequencies, circulating current, and power for SuperKEKB, NSLS-II, and ERL. Estimate charge interception, BPM analysis, and electron beam energy measurement.

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Homework Monday, June 15 th 2015

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  1. Homework Monday, June 15th 2015 #1 In an early design of the SuperKEKB project (asymmetric collider) the design single bunch populations were 5.25E10 (electrons) and 12E10 (positrons). The ring circumferences are 3016 m each containing 5000 bunches. Determine (a) the bunch spacing, (b) the bunch revolution frequency, (c) the bunch repetition frequency, (d) the total circulating current in each of the two accelerators. The beams are injected at full energy and relativistic. What are the total currents for the present design with per bunch currents of 1.04 mA (HER, electrons), 1.44 mA (LER, positrons) and 2500 bunches per ring?

  2. Early design: https://indico.cern.ch/event/47961/session/9/contribution/25/material/slides/3.pdf

  3. Present design: http://www-superkekb.kek.jp/documents/MachineParameters150410.pdf

  4. #2 This exercise is similar to the previous one, serves to illustrate different parameter ranges of circular lepton accelerators with different objectives. The new NSLS-II light source has a ring circumferences of 792 m and 1056 bunches. Determine (a) the bunch spacing, (b) the bunch revolution frequency, (c) the bunch repetition frequency, (d) the total circulating current. The beam energy is 3 GeV and is injected at full energy.

  5. #3 The European Spallation Source, ESS, in Sweden, the Facility for Rare Isotope Beams, FRIB, in Michigan, and the China Accelerator Driven System, CADS, planned for waste transmutation in China, all involve very high power beams. This exercise involves computation of beam powers with realistic constraints using as an example the BNL energy recovery linac (ERL). electron gun laser 5-cell cavity

  6. The beam power depends on average current which depends on duty factors, Fi P P = beam power Qb = charge per bunch flaser = laser repetition frequency V = gun voltage P = Qb flaser Fi V i I = Qb flaser Note P <I> = Qb flaser Fi i Calculate the average beam current and the total beam power for the following different possible modes of operation. • high current scenarios (uses 700 MHz laser, duty factor=1) with Qb=0.5 nC and • (i) 5-cell cavity off, so the beam energy is given by the gun • voltage V = 2.5 MV • (ii) 5-cell cavity on providing a total voltage to the beam (gun + • cavity) of V = 25 MV • high charge scenarios (uses 9.383 MHz laser, duty factor=1) • (i) with 5-cell cavity off • (ii) with 5-cell cavity on

  7. another scenario in which the gun is used as the electron source for low energy • cooling (uses 700 MHz laser, duty factor=0.43) and with • (i) 5-cell cavity off • (ii) 5-cell cavity on • Initial commissioning (here finding bunch structures suitable for so-called fault studies). Assume a laser frequency of 9.383 MHz, 5-cell cavity off, a gun voltage of 1 MV operating for 1 second intervals, a gun focussing solenoid operable for 5 s once every 5 minutes, and a maximum duration of bunches of 7 ms as limited by the current transformer used to measure the beam current.

  8. #4 Estimate the charge intercepted by a Faraday Cup (terminated into 50 W) based on the voltage signal below. BNL ERL (11/17/14)

  9. #5 At the Relativistic Heavy Ion Collider ~ 600 stripline BPMs (150/plane, two rings) are used to measure the orbits along the accelerator, examples are shown below. 4 km full scale The stripline length is ~ 25 cm and one end of each stripline electrode is grounded. The BPMs look like this: At 12 locations (on either side of each of the 6 interaction regions), the monitor detects beams travelling in opposite directions. The photograph shows such a measurement. (a) explain the polarities of the bipolar pulses (b) what is the distance of this BPM to the interaction point? (c) comment on the time separation between the peaks of the bipolar pulse

  10. (d) comment on the time separation between the peaks of the bipolar pulse for this 1 m stripline (non-IR BPM)

  11. #6 For the low-energy electron cooling project at RHIC (FY18-FY20), the relative energy (specifically velocity) difference between the to-be-cooled ion beams and electron beams is ~ 1E-4. This is very challenging. For the electron beam (only) calculate the time difference to be resolved for a time-of-flight based energy measurement assuming 1e-3 energy resolution, measured over 10 m with (a) g = 4 (b) g = 10 In practice, a distance between detectors of 10 m is impractical since the bunch length changes over this distance. Calculate the time difference assuming a separation between detectors of 2 ms with (c) g = 4, (d) g = 10 (e) Comment on the feasibility of this approach for determining the absolute electron beam energy.

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