Time Dependent Physics of Single Surface Multipactor
by Multiparticle Monte Carlo Simulations
Asif
1. Motivation
2. Single Surface Multipactor Susceptibility
Geometry
= 𝐸!"$ sin 𝜔𝑡 + 𝜃 + 𝛽𝐸!"$ sin 𝑛𝜔𝑡 + 𝜃 + 𝛾
𝐸# = normal electric field
𝜷 = relative strength of the 2nd carrier
mode
𝜸 = relative phase of the 2nd carrier mode
𝒏 = ratio of the two carrier frequencies
[need NOT be an integer]
𝜙 = initial angle of electron flight
𝑣$ = initial velocity
𝜉 = impact angle
Dual frequency susceptibility boundaries
"𝟏 ×
𝐄𝐦𝐚𝐱𝟎/𝟒𝟎𝟎𝐞𝐕
"𝟏/𝟐
𝜷 = 𝟏, 𝒏 = 𝟐, Relative phase 𝜸 is kept constant over time [4]
𝐄𝐫𝐟 [𝐌𝐕/𝐦]× 𝐟/𝟏𝐆𝐇𝐳
John
a,b
Verboncoeur ,
Peng
a
Zhang
3. Multiparticle Monte Carlo (MC) Model
Ø Multipactor [1,2] is a nonlinear phenomenon in which an
electron avalanche driven by a high frequency rf field sustains
itself by an exponential charge growth through secondary
electron emission from a metallic or dielectric surface
Ø Avoiding multipactor is a major concern for high power
microwave (HPM) sources, rf accelerators, and space-based
communication systems
Ø Study of the time-dependent physics [3] offers a better
understanding of the multipactor dynamics
Ø Multipactor susceptibility on a single dielectric surface for two
carrier frequencies [4] of the rf electric field is significantly
different from that of single carrier frequency
Ø RF fieldà 𝐸!"
a
Iqbal ,
Ø Previous MC models§ Single particle approach:
Simple implementation [1,2]
§ Variable number of particles
approach: Better statistics in
growing discharge [3]
Ø Multiparticle MC model§ large number of macroparticles
§ number of macroparticles kept fixed
§ charge in the impacting macroparticle changed and normal
electric field updated at each impact
§ less costly implementation than variable number of particles
approach, better statistics than single particle approach
§ time intervals between subsequent bounces of particles on
the surface calculated exactly
4. Simulation Results
Single frequency temporal study
Ø Single rf frequency operation:
"𝟏 ×
𝐄𝐦𝐚𝐱𝟎 /𝟒𝟎𝟎𝐞𝐕
"𝟏/𝟐
Ø Multipactor susceptibility boundaries depend on the relative
strength 𝛽 and relative phase 𝛾 of the second carrier mode
Ø The dependence of susceptibility boundaries on relative
phase 𝛾 is not as prominent as shown in ref [4]
Ø The conclusions of ref [4] about the trend of this dependence
remains valid
Square-shape rf field
Ø For 𝑓!" = 1𝐺𝐻𝑧, normal
surface field (𝐸# ) saturates
without oscillation
Ø For 𝑓!" = 10𝐺𝐻𝑧, prominent
glitches appear in the 𝐸#
curve when rf field switches
between positive and
negative levels
5. Conclusion
Ø For the dual frequency mode of the rf electric field, the
saturation level and oscillation pattern of the normal electric
field change from those of the single frequency mode
Ø These changes are due to the modification of the rf
envelope and the susceptibility boundaries of the dual
frequency mode
Ø Normal field profiles have been studied for square wave rf
field at different rf frequencies
6. Future Work
Ø Normal surface field (E# ) and secondary electron emission
(𝛿) oscillates at twice the rf frequency [3] in steady state.
Ø At saturation, 𝛿%&' = 1
Dual frequency temporal study
𝛽 = 1, 𝛾 = 0, 𝑛 = 2
Ø Temporal study for different combinations of relative strength
𝛽, relative phase 𝛾 and frequency ratio 𝑛 for dual frequency
operation
Ø Temporal study for different non-sinusoidal rf waveshapes
Ø Study of multi-frequency operation
7. Reference
𝜷 = 𝟏, 𝒏 = 𝟐, Relative phase 𝜸 evolves with time
𝐄𝐱[𝐌𝐕/𝐦]× 𝐟/𝟏𝐆𝐇𝐳
4. Simulation Results (continued)
Ø Temporal profiles of normal surface field (E# ) and secondary
electron emission (𝛿) oscillates at four times the fundamental
rf frequency, with 𝛿%&' = 1 at saturation
Ø Saturation level of normal surface field (E# ) higher than
single frequency operation
Ø Instantaneous E# stays at a lower value for longer duration
during an rf period
[1] R. A. Kishek and Y. Y. Lau, Phys. Rev. Lett. 80, 193 1998.
[2] L. K. Ang, Y. Y. Lau, R. A. Kishek, and R. M. Gilgenbach,
IEEE Trans. Plasma Sci. 26, 290 1998.
[3] H. C. Kim and J. P. Verboncoeur, Physics of Plasmas 12,
123504 2005.
[4] Asif Iqbal, John Verboncoeur, and Peng Zhang, Physics of
Plasmas 25, 043501 2018.
Work was supported by AFOSR MURI Grant No. FA9550-18-10062, and in part by an MSU Foundation Strategic Partnership
Grant.
(a) Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
(b) Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, MI 48824, USA
Email: iqbalas3@egr.msu.edu
johnv@egr.msu.edu
pz@egr.msu.edu