Electron Motion in a RF Cavity with external Magnetic Fields

Diktys StratakisBrookhaven National Laboratory

RF Workshop – FermiLabOctober 15, 2008

Introduction

• Asperities can arise from material imperfections on the cavity surface.

• At the tip of an asperity the field is enhanced. Emission of electrons is possible.

• Emitted electrons are accelerated by the RF field and can impact a wall far from the emission point.

• Strong external magnetic fields can act to focus the electrons to a particular point increasing the probability to damage there (surface heating, secondary emission).

• How space-Charge affects this process is still an open question

3

Objectives of this Study

• Model the propagation of field emitted electrons from asperities through an RF cavity. In the simulation we include:– RF and externally applied static magnetic fields– The field enhancement from those asperities– The self-field forces due space-charge

• Demonstrate a design of a magnetically shielded cavity

4

Simulation Tools at BNL

• CAVEL (R. C. Fernow - BNL)– 3D Code – Particle tracking within cavity fields and external fields

• PARMELA (LANL)– Can also do particle tracking within cavity fields and

external fields– Includes space-charge effects

• We successfully benchmarked those two codes (no space-charge)

Electron Tracking under External Fields (1)

• Electron is emitted from the location of maximum field enhancement (the cavity iris) and tracked at various RF phases.

• No space-charge included• In the presence of magnetic fields they get focused to a

particular point with large energies.

B=0 T B=1 T B=1 T, tilted

Electron Tracking under External Fields (2)

• Note the second peak in energy (green color)• Returning electrons can also damage the material

The Solution (?): Insulated 805 MHz Cavity

B. Palmer

Insulated 805 MHz Cavity

• Electrons are emitted normal to the surface at various phases

• Initial electron energy is 1 eV

• Maximum axial Field is 17 MV/m• All particles return to surface

with low energies

Test of Cavity Tolerances

d

• A cavity displacement greater than 2 mm reduces the efficiency of insulation

• Cavity becomes “more sensitive” to uncertainties at higher magnetic fields

Asperities in RF Cavities

• Assume: and 50c μm

• Then , consistent with experimental observations.

c

b

• Model asperity as a prolate spheroid. Then, the field enhancement at the tip is:

214eβ

20

02 (ln(2 ) 1)

TIP e

E cE β E

cb

b

2b μm

9 1.56.53 10

0.5 02 2

6 4.5201.54 10 10φ

β Eeφ ee eβ A EI

φ

• Dark current (Fowler-Nordheim model):

Field Enhancement around Asperity

z (μm)

R (

μm

)

0

EEE

0E: Enhanced field from asperity

: Local field (no asperity)

Simulation Details • Asperity is placed on the axis of a 805 MHz cavity• A 1mA, 1ev electron beam is uniformly distributed 1 μm

around the asperity tip.• A grid that is a superposition of the RF fields and the

asperity enhanced fields is used as the field map. • Gradient on axis is equal to 1 MV/m.• We have a uniform 1T external magnetic field.

c

b

805 MHz

Very Preliminary Results

• Electrons reach the other side of the cavity• They reach energies up to 1 MeV for both cases• Indeed space-charge is defocusing electrons, generating so

larger spots

With Space-ChargeNo Space-Charge

Outlook

• Further study is required. Issues to be addressed are: – Electron initial distribution – Beam Current– Asperity geometry– Multiple Asperities– External field orientation

Summary

• Field Emitted electrons were tracked with PARMELA under the influence of RF, static magnetic fields and self-fields (space-charge).

• Tested the efficiency of a 805 MHz magnetically insulated cavity.

• We collaborate with:– Tech X – Imperial College, Lancaster University: (A. Kurup, K. Long, R.

Seviour, A. Pozimski, A. Zarrebini)