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PSB magnetic cycle 160 MeV to 2 GeV with 2.5E13 protons per ring

Specifications 2.5E13 p from 160 MeV to 2 GeV Current in bending magnets < 2267 A RMS +10% = 2493 A RMS with 1.2 second cycle (no modification of the cooling circuit). B dot max = 38 G/ms assumed value {= 28 G/ms (present)* 5358 A (2GeV) / 4027 A (1.4 GeV)}

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PSB magnetic cycle 160 MeV to 2 GeV with 2.5E13 protons per ring

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  1. Specifications 2.5E13 p from 160 MeV to 2 GeV Current in bending magnets < 2267 ARMS +10% = 2493 ARMS with 1.2 second cycle (no modification of the cooling circuit). Bdotmax = 38 G/ms assumed value {= 28 G/ms (present)* 5358 A (2GeV) / 4027 A (1.4 GeV)} Cavity voltage and current taken as free parameters. Longitudinal space charge effects taken into account (assuming elliptic energy distribution) PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  2. Simplifications Pure h=1 acceleration Inductive and resistive wall effect neglected (impedance value to be asked for, but practically assumed to be low !?). The inductive effect counteracts the space charge effect. All these (pessimistic) simplifications lead to conservative figures PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  3. Longitudinal space charge effect Total coupling impedance: Z0 = 377 Ω Parasitic voltage superimposed (each turn) to the accelerating voltage (space charge only): PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring Inductive and resistive wall neglected Circular beam pipe approximation (real value to be checked for) 2 GeV magnetic cycle 12/05/2010

  4. Longitudinal space charge effect Parasitic voltage superimposed (each turn) to the accelerating voltage (space charge only): PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  5. Simulation 1: injection at 1.2 T/s, bucket filled up to 80 % with 2.5E13p (1.024 eV.s) PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring The acceleration lasts 330 ms with a 5 ms flat-top (490 ms presently) I MPS = 2341 ARMS (1.2 s cycle) < 2493 ARMS; Total magnetic cycle length from 0G to 0G = 700 ms with 38 G/ms max Bdot. 2 GeV magnetic cycle 12/05/2010

  6. Simulation 1: Limitation of Bdot to 38 G/ms (28 G/ms = present max) PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring The required h1 cavity current for the acceleration = 8.73 AP(present max = 3AP) DC current at 2 GeV= 7.2 A = 2.5E13*1.6E-19*1.8E6 MHz 2 GeV magnetic cycle 12/05/2010

  7. Simulation 1: The bucket is full (1.024 eV.s +20%) during the first 225 ms of acceleration PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  8. Simulation 1: The cavity voltage has been increased to compensate for space charge effects The net voltage experienced by the beam is 8 kV along the cycle PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring The required h1 cavity voltage is 11.3 kVP (present max = 8kVP). The beam h1 current goes up to 14.3 AP. This value is dealt with by the tuner loop (when there one!) 2 GeV magnetic cycle 12/05/2010

  9. Simulation 1: The beam peak-peak current goes up to 52.4 AP-P = 45.2 AP (52.4 – 7.2 DC). With a resonant cavity only, the h1 current was dealt with by the tuner loop. With a wideband cavity this current needs to be supplied! PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring With a narrow-band cavity, the beam-loading instability needs to be checked for. 2 GeV magnetic cycle 12/05/2010

  10. Simulation 1: PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  11. Conclusion: These simulations concerns h1 uniquely, for a single harmonic acceleration made as fast as possible with a 1.2 eV.s beam emittance and a max 38 G/ms Bdot . The requirement should be lessened (not much) in a dual harmonic context. The h1 cavity voltage should provide more than 11.3 kVP Its current available for acceleration should be higher than 8.73 AP (Narrow band cavity) It should deal with 45.2 AP of beam current (effective current with a wideband cavity, beam loading instability to be checked with narrow-band cavity) Slowing down the acceleration allows for a lower current demand in a narrow band cavity only. With the fast cycle which has been sketched, the power dissipation in the bending magnets is just below the maximum tolerated (2341 < 2493 ARMS). PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

  12. To be done: Make simulations with h=2 and more precise model of the MPS Check for beam loading instabilities with narrow band cavities Check transverse space charge effects PSB magnetic cycle160 MeV to 2 GeV with 2.5E13 protons per ring 2 GeV magnetic cycle 12/05/2010

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