Electron cloud effect for Linear Collider damping rings

1
Electron cloud effect for Linear Collider
damping rings

• K.Ohmi, KEK
• ECLOUD04,
• 19-23 April, 2004,
• Napa

2
Parameters
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
3
Electron 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

4
Multipacting from seed electrons

• Recently, M. Pivi et al. have studied
  multipacting condition from starting seed
  electrons.
• We first try to reproduce the results.

5
SEY and multipactoring
6
Requirement 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.

7
Synchrotron 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.

8
Electron 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)
10
Instability caused by electron cloud

• Coupled bunch instability
• Single bunch instability

11
Coupled 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

12
Medium range Wake force and growth of CBI (Fill
1.4ns)
ECLOUD 2002

• Wake force Mode stability

Growth time 20 turns 26ms
13
Medium range Wake force and growth of CBI

• Wake force Mode stability

99 protected (I,II) Growth 300ms
99.5 protected (II) Growth 600ms
14
Single 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)

15
Short 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 )

16
Threshold 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

17
Threshold cloud density of some positron rings
QMin(wesz/c, 5)
18
PIC 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.

19

• Particle In Cell method

Positrons 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
20
Characteristics 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.

21
Beam and cloud structures along z

• ns0 ns0.002

Tail Head
22
Growth of beam size

• Projected size along z

23
Scaling 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.

24
From 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.

25
Summary 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.

26
Summary 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).