Title: Electron cloud effect for Linear Collider damping rings
1Electron cloud effect for Linear Collider
damping rings
- K.Ohmi, KEK
- ECLOUD04,
- 19-23 April, 2004,
- Napa
2Parameters
GLC/NLC I GLC/NLC II TESLA
E (GeV) 1.98 1.98 5
Circum. (m) 395 300 17,000
N 0.75x1010 0.75x1010 2x1010
frep (ns) 1.4 1.4 20
sx (mm) 83 50 270
sy (mm) 7 6 270
sz (mm) 5 5.5 6
ns --- 0.0118 ---
rchamber(cm) 1 1 2.5
3Electron cloud build-up (EC2002)
- Ante-chamber R1cm, half width of slot 0.5 cm.
- In KEKB test ante-chamber, electron current 1/5
of cylindrical chamber was observed. - Average Photoelectron yield Y1g0.015 e-/(m.e)
for Yg0.65 g/(m.e). - (KEKB 0.015 e-/(m.e) for Yg0.15
g/(m.e)) - Peak secondary yield is assumed d21.0 e/e
4Multipacting from seed electrons
- Recently, M. Pivi et al. have studied
multipacting condition from starting seed
electrons. - We first try to reproduce the results.
5SEY and multipactoring
6Requirement for SEY
- GLC bend, dmax lt1.2-1.3.
- GLC drift, dmax lt1.4-1.5
- TESLA drift, dmax lt1.9
- Consistent with Pivis results
- dmax should be suppress to be around 1.2.
7Synchrotron radiation
- Yg0.65(I) or 0.86(II) g/(m.e),
- (KEKB Yg0.15 g/(m.e))
- Most of photons must be protected in slot of the
antechamber. - Angular divergence of synchrotron radiation
- K.J.Kim, S.
Kamada - uc1.75 keV at E1.98 GeV, B0.67T
- sy1 mrad for u10 eV.
8Electron density (EC2002)
20 of SR contributes. dmax lt1.
- Summary at 2002
- We need further reduction of the electron cloud
of 1/51/10. The electron yield per positron and
meter is required Y12lt0.002 e-/(m.e) for
suppress both of the coupled and single bunch
instability.
Synchrotron radiation should be protected much
more.
9- Assume that 99.5 of SR is protected by
antechamber slot. - Y1g3.3x10-4 e-/(m.e)
As shown latter, this cloud density level is
limit considering instability threshold.
Take care of electron flow from antechamber slot
(Liu,BEPC)
10Instability caused by electron cloud
- Coupled bunch instability
- Single bunch instability
11Coupled Bunch Instability caused by electron cloud
- Wake force is calculated by a numerical method as
follows, - Equilibrium electron cloud.
- A (i-th) bunch Dyi with a displacement passes
through the cloud. - Calculate kick Dpy,j of j-th bunch.
- Growth of the coupled bunch instability is
estimated by
12Medium range Wake force and growth of CBI (Fill
1.4ns)
ECLOUD 2002
- Wake force Mode stability
Growth time 20 turns 26ms
13Medium range Wake force and growth of CBI
- Wake force Mode stability
99 protected (I,II) Growth 300ms
99.5 protected (II) Growth 600ms
14Single bunch instability caused by electron cloud
- The single bunch instability is analyzed by wake
field method and tracking simulation. - Wake field
- Linearized model.
- Numerical calculation including nonlinearity.
(Similar way to the calculation of the
multi-bunch wake field)
15Short range wake field induced by electron cloud
- Short range wake for coasting beam
Analytical solution with a simplified linear
theory
- cR/Q1.4x107 m-2 (0.94x107 m-2)
- we (5.5x1011 s-1 )
16Threshold of fast head-tail instability
- Bounce frequency of electrons in the positron
beam potential - wesz/c9.5 (V)gtgt1 2.6 (H)gt1
- Coasting beam model
- Stability criteria
17Threshold cloud density of some positron rings
QMin(wesz/c, 5)
18PIC simulation (PEHTS)
- Transverse mesh. 2D electric field calculation
for electrons and positron bunch. Based on a
beam-beam simulation code for the strong-strong
model (BBSSP). - A bunch was sliced into 3050 in the longitudinal
direction. - A bunch interacts with electron cloud with a
projected density rexL for each traveling of L.
We choose LC circumference in this
presentation, and the case of more interaction
points in a ring LC/n is equivalent to lower
cloud density re/n.
19Positrons in a bunch and electrons in the cloud
are mapped on a 2D mesh. Electric potential is
calculated by solving the Poisson equation.
y
Cloud
x
Bunch
y
z
x
20Characteristics of the head-tail instability
- Dipole coherent motion along z.
- The instability is characterized by the wake
strength per a synchrotron phase advance. - The instability does not depend on the transverse
tune except for a special value, for example
synchro-beta resonance. - Beam size and coherent amplitude are comparable
before experience of strong Landau damping. - We can distinguish whether the instability
obtained by the simulation is head-tail type by
investigating the above characteristics.
21Beam and cloud structures along z
Tail Head
22Growth of beam size
23Scaling of ns and cloud density
- In the theory of the strong head-tail
instability, the instability should be scaled by
the ratio of the wake strength (cloud density)
and the synchrotron tune.
24From the results of the PIC simulation (for GLC I)
- Threshold of the strong head-tail instability due
to the electron cloud is around - re/ns 1012/0.01 m-3.
- Growth for re1012 m-3 is deviated from others,
namely the scaling is broken. - Kick due to cloud with the projected density rex
C is too strong. The instability occur due to
localization of the cloud, and may be not
realistic. - For the case that the electron cloud distributes
whole of ring, the coherent head-tail instability
is dominant.
25Summary I
- We assume primary electron yield Y1g 6.6x10-4
and 3.3x10-4 e-/(m.e) for GLC damping ring. This
value is 1 and 0.5 of the direct photoelectron
yield. - Electron cloud average densities are 0.8x1012 m-3
and 0.4x1012 m-3 for 1 and 0.5 SR ratio,
respectively. - The growth of the coupled bunch instability is
300ms and 600ms for 1 and 0.5 SR ratio,
respectively. - The growth can be recovered by bunch by bunch
feedback.
26Summary II
- The threshold cloud density of the fast head-tail
instability is re2.6x1012 m-3 for parameter I
(ns0.01) and re6.2x1012 m-3 for parameter II
(ns0.0118) in the linear wake approximation. - The wake approximation neglects some effects
nonlinearity, pinching of electrons - A PIC simulation has performed to study the
effects in detail. - The threshold of the fast head-tail instability
was re/ns 1012/0.01 m-3 for parameter I. It will
be higher for parameter II. - It is a factor 2-3 lower than that of the wake
approximation. This discrepancy is due to an
ambiguity or accuracy (pinching, choice of Q,
coasting beam approximation) of the wake
approximation. - Anyway, the threshold is higher than the density
of the present estimation based on our model
(assumption).