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