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Measurement of Resistivity Dominated
Collimator Wakefield Kicks at the SLC
M.Seidel, DESY
D. Onoprienko, Brunell Univ. UK, P. Tenenbaum, SLAC
June 4, 2002
• Motivation for the Experiment
• Principle of the Experiment
• Geometric and Resistive Wakefield Kicks
• Theoretical and Measured Results
• Discussion
M. Seidel, DESY, EPAC 2002
Motivation
• in linear colliders (also FEL’s) small gap collimation is needed;induced wakefields (geometric, resistive) are critical for beam emit-tance and lead to jitter amplification
• theory of short range wakefields is complicated; numerical calcula-tions are difficult
• measurements, if possible, are more direct !
• graphite as spoiler material is excellent from mechanical point ofview; low conductivity is one of the problems→ reliable predictionof resistive wall wakefield is important
M. Seidel, DESY, EPAC 2002
Spoiler and Absorber Concept
Beam
Spoiler Absorber
function: halo cleaning; machine protectionproblems: full beam survival; transverse wakefields
Typical Parametersat spoiler:
E ≈ 250 GeV
P ≈ 10 MW
σx × σy ≈ 150× 7µm2
spoiler gap ≈ 1 mm
spoiler thickness ≈ 0.5 radiation length
M. Seidel, DESY, EPAC 2002
Principle of the Experiment
• use the high quality damped SLC beam in sector II
• beam trajectory is measured upstream and downstream of the col-limator pair
• center of mass kick at collimator is determined for different verticalcenter offsets of the collimator
incoming Beam outgoing Beammovable Collimator
M. Seidel, DESY, EPAC 2002
Mechanical Layout
• aluminum cassette with 5 remotely interchangeable inserts
• precision vertical position adjustment
• beam view:
Cu C C
slot change movement
empty
roun
d slot
shor
t cop
per j
aws
shor
t grap
hite j
aws
long g
raphit
e jaw
s
unus
ed sl
ot
jaw vs beamadjustment
• short and long jaws:
8 inches 12 inches
M. Seidel, DESY, EPAC 2002
In Reality. . .
M. Seidel, DESY, EPAC 2002
Material Properties
we use a high density graphite with good vacuum properties(after baking at 400C)
Selected parameters for copper and graphite.
density conductivity skin-depth at[g/cm3] [Ω−1m−1] 500 GHz [µm]
Copper 8.9 5.9 · 107 0.1Graphite 1.95 5.5 · 104 3.0
M. Seidel, DESY, EPAC 2002
Beam Properties
• damped SLC beam at 1.19 GeV, γ = 2330
εx = 15 nm εy = 0.8 nmσx = 200µm σy = 50µmσz = 650µm
• bunch charge: 2 · 1010, 9Hz
• typical scan: 15 (vertical motion) × 25 (pulses); all automatedwith correlation plot feature of operating system
M. Seidel, DESY, EPAC 2002
Geometric Wakefield Kick
Transverse Geometric Wakefield Kick, averaged over Gaussian Bunch, see G. V. Stupakov,SLAC-Pub-8857 (2001)
θ
l_f l_t
g g_0
y_0
long taper:
for 0.2θth
2
σzg(≈ 18!) < 1 :
〈∆y′〉y0
=2√πθthNpreσzγg2
short taper - diffraction, neglects taper → expect overestimation:
〈∆y′〉y0
=4Npreγg2
M. Seidel, DESY, EPAC 2002
Resistive Wakefield Kick
see A. Piwinski, DESY-94 068 (1994):
θ
l_f l_t
g g_0
y_0
⟨∆y′⟩
=Γ(1
4)√
2
Npreγ
1√σzσZ0
·
lf sin(
2πy0
g
)+ 2πy0
g
g2(
1 + cos(
2πy0
g
)) +2lt
g0 − g
tan(πy0
g
)g
−tan(πy0
g0
)g0
⟨∆y′⟩
= a · y0 + b · y30 +O
(y5
0
)
→ use cubic fit-function
M. Seidel, DESY, EPAC 2002
Measured Deflection Curves
short graphite and Cu jaws
-6
-4
-2
0
2
4
6
8
-1.5 -1 -0.5 0 0.5 1 1.5
cm k
ick
angl
e [µ
rad]
gap position [mm]
Copperfit
short Graphitefit
long graphite jaws
-30
-20
-10
0
10
20
30
40
-1.5 -1 -0.5 0 0.5 1 1.5
cm k
ick
angl
e [µ
rad]
gap position [mm]
long Graphitefit
the fit functions contain a linear and a cubic term; the linear coefficientis compared to theory
M. Seidel, DESY, EPAC 2002
Comparison with Theory
Predicted geometric and resistive kick angles in [µrad/mm]:
collimator resistive part geom part sumtaper flat tot
short copper 0.001 0 0.001 6.7 6.7short graphite 0.67 0 0.67 6.7 7.4long graphite 0.67 6.1 6.8 6.7 13.5
Measured kick angles and inferred resistive part obtained by subtract-ing the kick of the copper jaws, in [µrad/mm]:
collimator measured total inferred resistiveshort copper 2.6±0.3 (0)
short graphite 3.9±0.3 1.3±0.6long graphite 10.8±0.4 8.2±0.7
M. Seidel, DESY, EPAC 2002
Discussion• result for graphite, gap width 3.8 mm, flat length of 4 inches, taper
angle of 10: w⊥ = 3± 0.3 V/pC/mm.
• geometric theory not well applicable for this taper angle; diffractionformula overestimates; resistive theory agrees relatively well
• graphite wakefield may be too strong for linear collider application→ coating or different material
• better faith in theoretical predictions for other materials
• planned: dependence on bunch length; smaller taper angles
Thanks to the colleagues atSLAC for the great collaborationon this subject!
M. Seidel, DESY, EPAC 2002