A few longitudinal BBU simulations
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A few longitudinal BBU simulations (in the SPL case) J-Luc Biarrotte CNRS, IPN Orsay. HOM excitation analyses. Beam flying ONCE through 1 cavity Allows to study when a HOM mode hits a beam spectrum resonance line Analytical power analysis is possible (&  sufficient)

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A few longitudinal bbu simulations in the spl case j luc biarrotte cnrs ipn orsay

A few longitudinal BBU simulations (in the SPL case)J-Luc BiarrotteCNRS, IPN Orsay


Hom excitation analyses
HOM excitation analyses

  • Beam flying ONCE through 1 cavity

    • Allows to study when a HOM mode hits a beam spectrum resonance line

    • Analytical power analysis is possible (&  sufficient)

  • Beam flying ONCE through N cavities

    • Allows also to study if a Beam Break-Up (BBU) rises « out from the noise »

    • Simulation is required (with very consuming CPU time)

  • (Beam flying N times through 1 cavity)

    • Non-Applicable to linacs


Input parameters for the spl case
Input parameters for the SPL case

  • PROTON BEAM

    • 352.2 MHz, 50 Hz, 5% d.c. (1ms pulse)

    • 150 MeV input energy

    • 400 mA mean pulse current

  • SC LINAC

    • 150 cavities @704.4 MHz

    • 20.7MV acc.voltage, -15° synch.phase (-> 3.15 GeV)

    • HOM mode considered:

      • 2000 MHz (far from main beam resonances)

      • Q=1E8 (no HOM coupler)

      • R/Q 50 ohms (very high, but will be kept for all simulations)


Errors distribution
Errors distribution

  • BEAM ERRORS

    • Bunch-to-bunch CURRENT normal fluctuation w/=10%*I0(120mA@3 )

    • Bunch-to-bunch input PHASE normal fluctuation w/=0.1° (1.2ps@3 )

  • LINAC ERRORS

    • Cav-to-cav HOM frequency spread (normal distribution) w/ =100 kHz(0.3MHz@3 )

    • Bunch-to-bunch cavity acc.voltage & phase normal fluctuations w/V=0%*V and =0°


Run i joachim s more or less
Run I (Joachim’s more or less)

 10 MeV

max Vhom: 3 MV

I0=400mA

I0=10%

0=0.1°

fHOM=2GHz

HOM=100kHz

QHOM=1E8

Vcav=0%

cav=0°

GROWTH

 10 MeV

 2.5°

GROWTH

 2.5°


Run ii meeting the real spl current
Run II (meeting the real SPL current)

max Vhom: 12 kV

I0=40mA : real current (400mA is anyway impossible to accelerate in SPL!)

I0=10%

0=0.1°

fHOM=2GHz

HOM=100kHz

QHOM=1E8

Vcav=0%

cav=0°

NO CLEAR GROWTH

 1 MeV

NO CLEAR GROWTH

 0.25°


Run iii with even more realistic inputs
Run III (with even more realistic inputs)

max Vhom: 1 kV

I0=40mA

I0=1% : 10% is a lot, especially considering bunch-to-bunch random fluctuations

0=0.1°

fHOM=2GHz

HOM=1MHz : closer to J-Lab or SNS data

QHOM=1E8

Vcav=0%

cav=0°

NO GROWTH

 1 MeV

NO GROWTH

 0.25°


Run iv the real spl
Run IV (the real SPL)

max Vhom: 4 kV

I0=40mA

I0=1%

0=0.1°

fHOM=2GHz

HOM=1MHz

QHOM=1E8

Vcav=0.3%

cav=0.3° : classical errors for (poor) LLRF systems

The same is obtained @ zero-current (w/o HOMs)

 10 MeV

 2.5°


A few longitudinal bbu simulations in the spl case j luc biarrotte cnrs ipn orsay

Run V (the real SPL w/ HOM couplers)

I0=40mA

I0=1%

0=0.1°

fHOM=2GHz

HOM=1MHz

QHOM=1E5

Vcav=0.3%

cav=0.3°

max Vhom: 300 V

w/ or w/o HOM couplers: SAME BEAM BEHAVIOR

 10 MeV

 2.5°


Run vi synchrotron like case
Run VI (synchrotron-like case)

I0=40mA

I0=1%

0=0.1°

fHOM=2GHz

HOM=0

QHOM=1E8

Vcav=0%

cav=0°

Always the same exact HOM freq => BEAM is QUICKLY LOST


Run vii synchrotron like case w hom couplers
Run VII (synchrotron-like case w/ HOM couplers)

I0=40mA

I0=1%

0=0.1°

fHOM=2GHz

HOM=0

QHOM=1E5

Vcav=0%

cav=0°

If no HOM spread at all => HOM coupler is required & efficient

 1 MeV

 0.25°


Run viii meeting a beam line w joachim s inputs
Run VIII (meeting a beam line, w/ Joachim’s inputs)

I0=400mA

I0=10%

0=0.1°

fHOM=2113.2MHz : the exact 6th beam line

HOM=100kHz

QHOM=1E8

Vcav=0%

cav=0°

Complete beam loss after only a few bunch


Run ix meeting a beam line more softly
Run IX (meeting a beam line, more softly)

I0=40mA

I0=1%

0=0.1°

fHOM=2113.2MHz

HOM=100kHz

QHOM=1E8

Vcav=0%

cav=0°

max Vhom: 4 MV

 10 MeV

 2.5°


Run x meeting a beam line even more softly
Run X (meeting a beam line, evenmore softly)

I0=40mA

I0=1%

0=0.1°

fHOM=2113.2MHz

HOM=1MHz

QHOM=1E8

Vcav=0%

cav=0°

max Vhom: 0.7 MV

 10 MeV

 2.5°


Run xi meeting a beam line w hom couplers
Run XI (meeting a beam line, w/ HOM couplers)

HOM excitation (W) Vs frequency on a beam spectrum line for different QHOM

max Vhom: 0.4MV

I0=40mA

I0=1%

0=0.1°

fHOM=2113.2MHz

HOM=100kHz

QHOM=1E5

Vcav=0%

cav=0°

High HOM power has anyway to be handled

 10 MeV

 2.5°


Conclusions personal draft for discussion
Conclusions (personal draft – for discussion !)

  • In SPL-like linacs, BBU « out from the noise » can be damped:

    • N°1: lowering QHOM (e.g. using HOM couplers)

      This is the only solution for extreme conditions (100’s mA with high fluctuations, low HOM dispersion... ) or in circular machines (zero HOM frequency spread)

      OR

    • N°2: naturally

      Simply checking that HOM modes are sufficiently distributed from cavity to cavity (=100kHz seems even to be enough in the SPL case)

  • Simulating the SPL case without HOM couplers & with realistic input parameters shows apparently no longitudinal Beam Break Up instability rising

  • Cavities should be designed to avoid having a HOM mode exactly matching a beam resonance line.In the case where this is NOT achieved:

    • Without HOM couplers (high QHOM): very low probability to really hit the resonance, but could lead to a cavity quench + beam loss if it happens -> CURE = simply measure all cavities before installation to check

    • With HOM couplers (low QHOM): the probability to hit the resonance is far larger but not catastrophic -> HOM couplers have to be designed to evacuate large HOM powers continuously


Limits of these non definitive conclusions
Limits of these non-definitive conclusions...

  • Very poor statistics : more simulations should be performed

  • 10X pulses should be simulated to confirm the behavior with a « quasi-infinite » pulse train, and to check if any instability linked with the pulse structure is rising (even if for SPL, it is a priori non-relevant for such low pulsing frequencies)

  • The real SPL linac layout should be taken as input, including, for each cavity family, all HOM properties (f, Q, r/Q())...

  • More realistic (non-white) noises should be considered

  • Being aware that all this would imply enormous CPU time...