New tool for beam break-up analysis

1
New tool for beam break-up analysis
TM110
y
y
2nd pass deflected beam
z
x
injected beam
E
B

• Reasons for writing a new code
• TDBBU weaknesses
• need for new features
• need for an in-house code

2
bi - beam instability code

• Features
• allows any ERL topology
• cleaner algorithm than TDBBU (very likely a
  personal bias)
• written in C (compiles with GNU GCC, i.e. all
  major OS)
• faster than TDBBU (a single 5 GeV ERL run takes
  less than a minute execution time is estimated
  to be 7-9 times faster than TDBBU when no
  coupling is present with coupling it is
  estimated to be at least 4 times faster)
• easier to use

3
Basic algorithm
Expand beam line into a consecutive list of
cavities (pointers) in the same order a bunch
sees them in its lifetime (from injection to
dump) Link pointers to actual HOMs Start
filling beam line with bunch train Determine
which pointer sees a bunch next Update
wake-field in HOM which is pointed by the
pointer Push the bunch to next pointer, store
its coordinates until they are needed by any
bunch that will reach this point next
consecutive list of cavities
1
2
3

N 2
N 1
N
actual HOMs (n ? N)
hom 1 hom 2 hom (n 1) hom n
4
Wake arithmetics
Wake function due to single bunch Electrons
in test bunch will get a kick Same for
test bunch trailing behind a bunch train qn,
dn
e
t
t
5
Horners trick
Problem evaluate polynomial an xn an1 xn1
a1 x a0 Correct answer ((anx an1) x
an2) x ) x a0 In the same
vein Introduce complex kick from
HOM CPU expenses then become linear with the
size of the problem
6
findbi utility to find threshold

• Features
• uses amplitude of complex kick due to HOM to
  determine whether case is stable
• uses bisection method to find threshold until
  derivative of wake amplitude growth rate vs. beam
  current stabilizes, then uses Newton-like method
• finds threshold with 0.1 accuracy in a typical
  ?? 8 iteration calls

7
Calibration single HOM recirculator
1st order perturbation approach fails
8
HOM frequency randomization (fixed current)
rms 0 Hz rms 33 kHz rms 42 kHz
rms 46 Hz rms 53 kHz rms 67 kHz
9
Simulation example ERL in CESR tunnel
single worst HOM R/Q 51.5 ?, Q 50000, f
2575 MHz frequency spread applied (rms) 3
MHz smallest threshold found so far 163
mA (linac lattice DCS, 04/01/03, max beta 80 m)
10
HOM displacement effect

• No change in threshold due to displacement
  errors is observed.
• There is emittance growth when operating near
  the threshold.
• Average kick amplitude grows.