Modeling of beam loss induced vacuum breakdown

1
Modeling of beam loss induced vacuum breakdown

• E.Mustafin, P.Spiller, GSI Darmstadt
• W.Fischer, U.Iriso, BNL Brookhaven
• ICFA HB-2004, Bensheim,
• October 18-22, 2004

2
Basic equation
c is specific conductance, q and q? are thermal
and desorption outgassing, s is linear pumping
speed, v is volume per unit length. The equation
must be solved with periodic boundary conditions
for the space coordinate and initial condition
for the time coordinate. (one more term will be
introduced later in the presentation)
3
The desorption term
h is the desorption coefficient, s is the
charge-exchange cross-section, N is the number
of beam ions, T is the beam revolution time.
G(x,x) describes how many of beam ions
experienced charge-exchange at position x do
arrive at the vacuum chamber wall into the slice
dx at the position x. Since all lost ions will
eventually reach the vacuum chamber wall the
function G(x,x) is chosen to be normalized
4
Meaning of the G(x',x) function
5
Equation with the desorption term

• Three applications of this equation will be
  considered further
• Elimination of dependence on the space coordinate
  study of the vacuum pressure averaged along the
  orbit and application to the pressure rise in the
  SIS18 of GSI Darmstadt,
• Elimination of the time dependence study of the
  steady-state vacuum pressure profile in
  application to the U beam in the SIS18.
• Addition of the surface stay term in application
  to the BNL vacuum pressure bump experiments.

6
System of equations for the average pressure
here nL2.7?1025 m-3 is the number of molecules
in cubic meter in normal conditions. Stability
condition hsN/T lt seff or hsNbc lt
Stotal Vacuum pressure in the stable condition P
P0 / (1 - ?sN?c/Stotal)
7
U28 ions circulating in SIS18 at constant energy
P0, t0
Pe lt P0, te gtt0
P gt P0, tltt0
8
Pressure evolution in the SIS18 derived from the
measurement and from the fit
9
Fitting U28 lifetime in the SIS18
E.Mustafin, O.Boine-Frankenheim, I.Hofmann,
H.Reich-Sprenger, P.Spiller, "A theory of the
beam-loss induced vacuum instability applied to
the heavy-ion synchrotron SIS18", NIM A 510
(2003) pp. 199-205.
10
Equation for the steady-state pressure profile
The equation must be solved with periodic
boundary conditions.
11
Self-consistent profile of losses in the SIS18
with the collimators at each vacuum pump position.
QUADRUPOLE TRIPLET
DIPOLE
DIPOLE
collimator pump positions in the SIS18
12
Simplification of the G(x',x) function and the
lumped pumping case
13
Special case losses on the collimators
14
Intensity limitation with collimators in the SIS18
15
RHIC pressure bump experiment with closed valves
Layout of vacuum equipment G denotes gauges, P
pumps, V valves, RGA a rest gas analyzer, and IP
the nominal beam interaction point. On the left
hand side is a 5.85 m section with activated NEG
coating.

• Measurement 1 valve V1 is closed, Blue beam
• Measurement 2 valve V1 is closed, Yellow beam
• Measurement 3 valve V2 is closed, Blue beam
• Measurement 4 valve V2 is closed, Yellow beam
• Pressure bumps were observed in gauges G2 G3

W.Fischer et al,. being prepared for publishing
16
Pressure bumps at RHIC with closed valves
17
Application to the RHIC experiment
Desorption yield values obtained from the G2
readings assuming the desorption spots at the
valves V1 and V2.
Desorption yield values obtained from the G3
readings assuming the desorption spots at the
valves V1 and V2.
G2
V1
G3
V2
Yellow
Blue
18
The scheme of another pressure bump experiment at
RHIC
U.Iriso et al., (almost ready to be published as
a BNL internal note)
19
A direct application of the diffusion equation
gave a discrepancy with the measurement
20
Diffusion equation with account of surface stay
time

here P(t-t) describes the release of stacked
molecules after surface stay time t.
here we used the fact that the surface stay time
is much shorter than any time scale under the
consideration
21
A fit with the modified diffusion equation in two
gas components approximation
22
Parameters extracted from the fit. The desoption
yield values are in the range of 3?104
23
Summary

• The use of the diffusion type equation to
  simulate the vacuum pressure evolution has been
  proven to be a fruitful approach in theoretical
  consideration of the vacuum breakdown description
  in the heavy-ion machines.
• The proposed method allows to describe the vacuum
  instability development, steady-state vacuum
  pressure profiles and the other phenomena related
  to the beam-loss induced pressure rise.
• Further work is necessary to determine
  experimentally the phenomenological parameters of
  the theory