electron motion in a rf cavity with external magnetic fields diktys stratakis brookhaven national...
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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)