Transcript jlablogo - Cornell University

New tool for longitudinal BBU simulations
monopole (m = 0)
R56
y
injected
beam
2nd pass
deflected
beam
TM01-like
y
z
E
x
B
high losses, no kick
Longitudinal BBU
• interaction with monopole modes through arc’s R56
• worst case threshold is given by
I th 
CHESS / LEPP
2 Ec
1
e( R / Q )  Q   R56
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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Implementation of the code
Features:
• allows any ERL topology
• arbitrary bunch pattern
• implemented by using Standard Template Library (STL) of C++
Performance
• surprisingly fast (0.1 ms of 5 GeV ERL takes ~ 1 min on my 800 MHz laptop)
• clear and concise code
CHESS / LEPP
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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Benchmarking
E = 30 MeV, (R/Q) = 100, Q = 10000, R56 = –10 m, tr = 10t0
1000
threshold current [mA]
tracking
100
formula
10
1
1
10
100
HOM frequency [GHz]
CHESS / LEPP
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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Some features of the longitudinal instability
0.8
•
I = 22.0 mA
0.6
similar to transverse BBU in
its scaling:
 [(R/Q)Q]–1, E
0.4
0.2
0
-0.2
-0.4
•
“bad” frequencies (n + ¼)0
does not grow exponentially,
but saturates
-0.6
arrival time difference [ps]
•
-0.8
3 0
50000
100000
150000
I = 22.1 mA
2
1
0
-1
-2
-3
10
8
6
4
2
0
-2
-4
-6
-8
-10
0
50000
100000
150000
I = 23.0 mA
0
50000
100000
150000
bunch #
CHESS / LEPP
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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Instability vs. Resonance
HOM-induced energy difference [eV]
10000
I = 23.0 mA
5000
13.0325 GHz
0
-5000
-10000
-15000
-20000
13.0 GHz
-25000
0
50000
100000
150000
bunch #
CHESS / LEPP
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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Outlook
•
•
•
have all the necessary in-house tools to simulate long-range HOM interaction
with the beam in ERL (e.g cumulative effects, multipass BBU)
useful to simulate transients (ion gap, start-up), beam induced power, etc.
study of possible feedback remedy for BBU
full longitudinal–dipole–quadrupole wake interaction (e.g. through dispersion
in the linac)
induced energy at the last HOM [eV]
•
15000
recirculation time
10000
5000
0
-5000
beam is on for 20 s
-10000
-15000
-20000
-25000
0
2
4
6
8
10
12
14
16
18
20
time [s]
CHESS / LEPP
Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003
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