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4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

SIMULATIONS OF MULTIPACTOR ZONES

TAKING INTO ACCOUNT REALISTIC PROPERTIES

OF SECONDARY EMISSION

A. Sazontov(1), N. Vdovicheva(2), M. Buyanova(1),

V. Semenov(1), D. Anderson(3), J. Puech(4),

M. Lisak(3), L. Lapierre(4)

(1) Institute of Applied Physics, Russian Academy of Sciences,

Nizhny Novgorod, Russia,

(2) Institute for Physics of Microstructures, Russian Academy of Sciences,

Nizhny Novgorod, Russia,

(3) Department of Electromagnetics, Chalmers University of Technology,

Gothenburg, Sweden,

(4) Centre National d’Etudes Spatiales,Toulouse, France


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

1. Motivation

2. Background

3. Effects of velocity spread

and high secondary

emission yield

Outline of talk

4. Threshold value of the secondary emission yield

5. Multipactor charts for realistic material properties

6. Summary

Uncertainty with multipactor charts

7. Simulations of the multi-carrier regime

Model, Resonance, Stability, Key parameters,

Separated charts, Hybrid modes

Perturbation of resonance,

Possibility to sustain

the unstable regime of multipactor


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

lgU

Motivation

Geometry and Main parameters

E 0sin(ωt)

RF Voltage U

RF Frequency ω=2πƒ

Gap width L

Schematic view of the Multipactor charts

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Hatch & Williams, Phys. Rev. 1958,

Woode and Petit, ESA Journal 1990

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Shemelin, Sov.Phys.Tech.Phys. 1986,

CNES Report No. 83


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Simple theory

• Important parameters of electron motion:

Amplitude of electron velocity oscillations in RF field V ω = eE 0 /mω

Initial phase of electron motion ϕ 0

Electron initial velocity V 0

• Classical Resonance

(one-way transit time equals

odd number of RF half-cycles)

• Stability condition

• Hybrid Resonance

(a number of RF

halfcycles coincides

with a duration

of a sequence

of electron transits)

⎛ V ⎞ 0

2sinϕ

0 +


⎜cosϕ

0 + ⋅ pk =

V ⎟


? ⎠

k = 2p −1,

p = 1,2,3,...

ϕ

min

⎛ V


⎝ V

0

?


, k ⎟ ≤ ϕ


0

?L

V

?

=

?(k),

⎛ 2

≤ atan⎜

⎝πk

~

~ ⎛ p ~ ⎞

?

~ ~

classical(

k ) ≤ ? hybrid ≤ ? classical(

k ) + ⎜ −ϕ

0 ⎟ ⋅cosϕ

0-sinϕ

0 + 1,

⎝ 2 ⎠

~

k = min(k1,

k2,

..., kn

), n is the order of a hybrid mode

~

~

ϕ is the start phase for transit with k RF halfcycles

0

Gilardini, J. Appl. Phys. 1992, 1995;

Kryazhev et.al., Physics of Plasmas, 2002




4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Resonant bands of key parameter l=wL L / V w


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

t 1

Perturbation of resonance

due to electron velocity spread

j R

EDF

t 2 >t 1

j 0

• Electron velocity spread results

in a spread of electron transit time

• Electron bunching around the stable

resonant phase is destroyed when

Evolution of electron

distribution function (EDF)

around stable resonant phase

δϕ

δV

V

ω


0

π

2


k 0




δV


V

ω

2 ⎞

⎟⎠

πk

2


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Effect of high secondary emission yield

t 1

j R

EDF

t 2 >t 1

j 0

EDF evolution around

unstable resonant phase

(case of relatively low

secondary emission: σ≈1)

t 1

j R

EDF

t 2 >t 1

j 0

EDF evolution around

unstable resonant phase

(case of high

secondary emission: σ>>1)


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Numerical simulation of multipactor

Particle-In-Cell code simulates realistic dynamics of

electrons taking into account the effects of space

charge but requires tremendous computer time.

Monte-Carlo code accumulates calculations of great

number of separate electron trajectories. It is relatively

fast but does not allow to take into account the effects

of space charge.

Statistical code calculates an evolution of EDF in

undisturbed RF field. It is very fast in case of simple

geometry and monochromatic RF field because a

considerable part of calculations can be done analytically.


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distribution

Threshold value of secondary emission yield

function :



V

F(

V0)

∝ exp −


⎝ 2V

velocity

2

0

2

T




σ threshold vs. λ calculated for different values of V T / V ω .

Solid blue lines represent the statistical approach, circles represent the

Monte-Carlo method results. The shaded areas indicate regions of

parameters where multipaction takes place.


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

Threshold value of secondary emission yield

function :

⎛ V

⎜ 0 exp



⎝ 2V

2

∝ 2

T

velocity




The comparison of statistical approach results with analytical

calculations of multipactor regions bounds.

•Each green line

represents the lower bound

both for a classical mode

and adjusted hybrid region

•Each blue line represents

the upper bound for a

classical mode

•Each red line represents

the upper bound for a

hybrid modes region


Threshold value of secondary emission yield:

PIC simulations

The step approximation of

secondary emission curve

was used:

σ

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

( ) ⎨

⎩ ⎧

V =

impact

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

σ

0

velocity

function :

0,

= const,

if V

impact

if

V

V 1 corresponds to25 eV,

V T corresponds to 3 eV

2




< V

impact

1

> V

1


Threshold value of secondary emission yield:

PIC and Monte-Carlo Monte Carlo simulations comparison

The step approximation of secondary

emission curve was used:

σ

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

F(

V

0

)

( ) ⎨

⎩ ⎧

V =

impact

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

σ

0

velocity

0,

= const,

if V

impact

if

V

V 1 corresponds to25 eV,

V T corresponds to 3 eV

2




distributi on

< V

impact

function :

1

> V

Threshold value of secondary emission yield

vs. λ for two values of V T / V ω using the

statistical method (solid blue lines)

and the Particle-In-Cell simulations (circles).

The shaded areas indicate regions of

parameters where multipaction takes place.

1

(a)

(b)


0

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

)

function :

⎛ V

⎜ 0 exp



⎝ 2V

2

∝ 2

T

velocity

Vaughan’s approximation*

of secondary emission curve

was used:

E max = 443 eV,

σ max was computed as the

threshold value;

V T corresponds to 3 eV.

*J. R. M. Vaughan,

IEEE Trans. Electron Devices

35, 1172 (1988).




Multipactor chart: PIC simulations


2

mV 2 = 3443

Tm

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

Multipactor chart: Statistical code calculations

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

velocity

function :

2




Vaughan’s approximation of secondary emission curve was used.

material properties:

V

1

is

Al AA2024,

thevelocity

corresponding

σ

max

=

1.

32,

2

mV 2 = 57 eV,

tofirst

cross - over point

Scientific parameter space Engineering parameter space

1


2

mV 2 = 3443

Tm

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

Multipactor chart: Statistical code calculations

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

velocity

function :

2




Vaughan’s approximation of secondary emission curve was used.

material properties:

V

1

is

OHFC Cu,

thevelocity

corresponding

σ

max

to first

=

1.

75,

cross-

2

mV 2 = 40 eV,

1

over point

Scientific parameter space Engineering parameter space


2

mV 2 = 3443

Tm

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

Multipactor chart: Statistical code calculations

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

velocity

function :

2




Vaughan’s approximation of secondary emission curve was used.

material properties:

V

1

is

OHFC Cu,

thevelocity

corresponding

σ

max

=

1.

99,

2

mV 2 = 30 eV,

to first cross -over

point

Scientific parameter space Engineering parameter space

1


2

mV 2 = 3443

Tm

4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Electron' s initial

distributi on

F(

V

0

)

Multipactor chart: Statistical code calculations

⎛ V

⎜ 0 exp



⎝ 2V

∝ 2

T

velocity

function :

2




Vaughan’s approximation of secondary emission curve was used.

material properties:

V

1

is

OHFC Cu,

thevelocity

corresponding

σ

max

=

2.

25,

2

mV 2 = 25eV,

to first cross - over point

Scientific parameter space Engineering parameter space

1


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Summary

σ 1.

32

75 . 1 σ

max =

max =

σ 1.

99

σ 2.

25

max =

max =


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

E

E

ω

k

k

n

= ∑

k = 1

E

k

Multi-carrier Multi carrier regime

cos( ω t + ϕ

is the amplitude of

− frequency, ϕ

k

k

k

) ,

a

− initial

carrier,

phase

In common case the predictions of

multipactor development and suppression

are very problematic: electrons dynamics is

rather sensitive even to a small change of

carriers parameters. Numerical simulations,

taking into account all actual parameters of

the system, are necessary.

lgU

lgƒL


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Multi-carrier Multi carrier regime: PIC simulations


4th International Workshop on Multipactor, Corona and Passive Intermodulation in Space RF Hardware

Carriers parameters:

Number

of carrier

Multi-carrier Multi carrier regime: PIC simulations

RF voltage

amplitude, V

(a) (b) (c)

Frequency, Initial Frequency, Initial Frequency, Initial

GHz phase GHz phase GHz phase

1 562,34 10.9 0 10.9 0 10.9 0

2 559,34 11.01 0 11.01 0.9476 10.922 0.9476

3 556.5 11.12 0 11.12 0.5175 10.944 0.5175

4 553,8 11.23 0 11.23 0.2130 10.966 0.2130

5 551.24 11.34 0 11.34 0.5375 10.988 0.5375

6 548.82 11.45 0 11.45 1.884 10.1010 1.884

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