Measurement of Resistivity Dominated Collimator Wake eld...
Transcript of Measurement of Resistivity Dominated Collimator Wake eld...
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