1. 2006. 08. 29 H. C. Kim, Y. Chen, and J. P. Verboncoeur Dept. of Nuclear Engineering, UC Berkeley CCP 2006 (S05-I22: Invited Talk) Modeling of RF Window Breakdown Transition of window breakdown from vacuum multipactor discharge to rf plasma Modeling of RF Window Breakdown Transition of window breakdown from vacuum multipactor discharge to rf plasma

2. Topic 0. 0. Introduction and Models I. Vacuum Multipactor Discharge II. Transition to RF Plasma

3. Undesirable Discharge in HPMs RF Window (Dielectric) Incoming EM wave RF generator (e.g. Magnetrons, Linear beam tubes, Gyrotrons, Free-Electron Lasers, and so on) Outgoing EM wave Conductor (High-Power Microwave) > Either Vacuum or Background Gas z y x z : direction of wave propagation  Discharge can degrade device performance or even damage devices, including catastrophic window failure.

4. In Vacuum (Multipactor Discharge) - - ++++++++++ - - -  Multipactor discharge* is an avalanche caused by secondary electron emission. Vacuum * Observed in various systems (e.g. RF windows, accelerator structures, microwave tubes and devices, and rf satellite payloads) Single-surface multipactor on a dielectric : leads to electron energy gain. : makes electrons return to the surface. (= life time) (TE or TEM mode) (maximum distance)

5. Analytic Solution of Single Particle Motion  Solution of the equation of motion for the electron in Vacuum The z- and y-components of the impact electron energy v x,0, v y,0 : initial velocity of the electron emitted from the surface  0 : initial phase of the rf electric field at that time (t=t 0 ) - - For the constant E z = E z0 during the flight, (TE or TEM mode)

6. With Background Gas (RF Plasma) - - - - - + + + + + +  Under the high-pressure background gas, an rf plasma is formed.  The rf plasma is a candidate for window breakdown on the air side.  Under the high-pressure background gas, an rf plasma is formed.  The rf plasma is a candidate for window breakdown on the air side.

7. Discharge Sustainment  Electron generation mechanisms in the system Secondary Electron Emission (SEE) on a surface originated from electron impact to a material : Dominant in Vacuum or under the low-pressure gas Ionization in the volume originated from ionization collisions between electrons and the background gas : dominant under the high-pressure gas - - + - - - - probabilistic event Another emission mechanisms: thermionic emission, photo emission, field emission, explosive emission, and so on. +

8. Secondary Emission due to Electron Impact - i, (Electron Impact Energy)  (Electron Impact Angle) [Ref] Vaughan et al, IEEE (1989); IEEE (1993)  Energy and angular dependence of secondary emission yield (the ratio of the incident flux to the emission flux)

9. 1D3V Particle-In-Cell (PIC) Model - - ++++++++++++++++++ - - - Dielectric y x L (δ=0) - - - - Condition of left dielectric + + + +  Simulation Tool : Modified XPDP1 from PTSG, UC Berkeley [Ref] J.P. Verboncoeur et al., J. Comput. Phys. 104, 321 (1993)

10. Topic I. * Our model is based on electrostatic fields and the magnetic field is not taken into account. 0. Introduction and Models I. Vacuum Multipactor Discharge II. Transition to RF Plasma

11. Dynamics using Monte-Carlo Simulation* * [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998) Problem: No oscillation appears even though Discharge off : low  due to Too high impact energy Too small impact energy Discharge on (Positive growth rate)  Susceptibility Curve for Plane Wave

12. Model of Monte-Carlo Simulation Emission of initial seed electrons from the surface v z,0, v y,0 : Maxwellian distribution  : Uniform distribution → Calculate the impact energy and angle (from analytic solution of one particle motion) → Calculate the secondary electron yield (from model of SEC due to electron impact) Ejection of multiple secondary electrons (N n+1 ) from the surface v z,0, v y,0 : (from the energy distribution of secondary electrons)  : The phase of next injection is taken from the phase of impact for the parent electron. Update * [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998)

13. [Ref] H.C. Kim and J.P. Verboncoeur, Phys. Plasmas 12, 123504 (2005) Dynamics using PIC Simulation PIC simulation shows that the electron number and the E z oscillate at twice the rf frequency, saturating after 1 ns. E z oscillates in and out of the susceptibility region. PIC simulation shows that the electron number and the E z oscillate at twice the rf frequency, saturating after 1 ns. E z oscillates in and out of the susceptibility region. (solving field eqn. self-consistently) Plane Wave

14. PIC: Susceptibility Curve (Plane vs. TE 10 ) ~ x 1.5 TE 10 mode Plane wave In TE 10 mode, the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant. TE 10 mode Effect of transverse field structure z : direction of wave propagation

15. Summary for Topic I In HPM systems, the time-dependent physics of the single-surface multipactor has been investigated by using PIC simulation.  The normal surface field and number of electrons oscillate at twice the rf frequency. The effect of the transverse field structure on the discharge has been investigated.  In TE 10, the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant.

16. Topic II. 0. Introduction and Models I. Vacuum Multipactor Discharge II. Transition to RF Plasma

17. Collision with Argon Background Gas Electron-Neutral Collision Ion-Neutral Collision  The argon gas is used in this study because of its simplicity in the chemistry (compared with air).

18. PIC: Number of Particles (I) The number of electrons still oscillates as in the vacuum case but increases slowly in time, as a result of electron-impact ionization. # of ions ~ # of ionization events between electrons and argon gas Vacuum multipactor discharge The secondary electron emission is the only mechanism for generating electrons. Vacuum multipactor discharge The secondary electron emission is the only mechanism for generating electrons.

19. PIC: Number of Particles (II) The numbers of electrons and ions are nearly the same and increase abruptly in time. Collisional ionization becomes the dominant mechanism to generate electrons. The numbers of electrons and ions are nearly the same and increase abruptly in time. Collisional ionization becomes the dominant mechanism to generate electrons.

20. PIC: Electron Mean Energy Electrons in the multipactor discharge gain their energy by being accelerated from the rf electric field during the transit time. At high pressures, electrons suffer lots of collisions and lose the significant amount of energy gained from the rf electric field.

21. PIC: Electron Energy Distribution Below 50 Torr, the EEPF is bi-Maxwellian type. At high pressures, the EEPF becomes Druyvesteyn type since the electron temperature decreases with the collision frequency. Below 50 Torr, the EEPF is bi-Maxwellian type. At high pressures, the EEPF becomes Druyvesteyn type since the electron temperature decreases with the collision frequency. Spatially averaged

22. PIC: Electron and Ion Densities * Time-averaged over a cycle At low pressures, the multipactor discharge is formed near the dielectric window. At intermediate pressures, both multipactor discharge and rf plasma exist. At high pressures, only rf plasma is formed, away from the surface of the window. At low pressures, the multipactor discharge is formed near the dielectric window. At intermediate pressures, both multipactor discharge and rf plasma exist. At high pressures, only rf plasma is formed, away from the surface of the window.

23. PIC: Electric Field Profile At low and intermediate pressures, the electric field is positive on the surface, indicating that the multipactor discharge can be sustained. At high pressures, the electric field is negative on the surface. The energy of electrons impacting the surface is low enough so that the secondary electron emission yield is less than 0.5. At low and intermediate pressures, the electric field is positive on the surface, indicating that the multipactor discharge can be sustained. At high pressures, the electric field is negative on the surface. The energy of electrons impacting the surface is low enough so that the secondary electron emission yield is less than 0.5.

24. PIC: Secondary Electron Emission  Secondary electron emission yield on the dielectric * For particles accumulated over a cycle Below 10 Torr, the secondary yield is near unity so that multipactor discharge can be sustained. As the pressure increases, collisions suppress the impact energy and hence the secondary electron yield  decreases to less than unity. Below 10 Torr, the secondary yield is near unity so that multipactor discharge can be sustained. As the pressure increases, collisions suppress the impact energy and hence the secondary electron yield  decreases to less than unity. Transition Pressure (10~50 Torr) surface discharge is collisionless. EEPF of rf plasma is Druyvesteyn.

25. Experiment for the Breakdown on the Air Side  The HPM surface flashover experiments at Texas Tech Univ. [Ref] G. Edmiston, J. Krile, A. Neuber, J. Dickens, and H. Krompholz, “High Power Microwave Surface Flashover of a Gas-Dielectric Interface at 90 to 760 Torr,” IEEE Trans. Plasma Sci. (to be published). Absorbed P = Incident P – Transmitted P – Reflected P Incident P Transmitted P Reflected P Flashover delay time

26. Experiment for the Breakdown on the Air Side 3 MW 3 MW, UV 4.5 MW is universal for different E rf0 at the given pressure range. Simple theory : L. Gould and L. W. Roberts, J. Appl. Phys. 27, 1162 (1956). f = 2.85 GHz Air: 90 ~ 760 Torr

27. PIC: Discharge Formation Time (I)  Simulation results of argon gas for various E-fields and frequencies At very high pressures, is universal for different E rf0 and . At very low pressures

28. PIC: Discharge Formation Time (II)  Simulation results of argon gas for various E-fields and frequencies At low pressures, is universal for different E rf0 and .  [ns]

29. Summary for Topic II In HPM systems, adding an argon background gas, we have investigated the transition of window breakdown from single-surface vacuum multipactor discharge to rf plasma. There is an intermediate pressure regime where both multipactor discharge and rf plasma exist. In our parameter regime, the transition pressure (  less than unity) is between 10 and 50 Torr in argon. The discharge formation time (  ) has been obtained as a function of the gas pressure. The normalization predicted by the simple theory holds only at very high pressures. At low pressures, the discharge formation time is independent of E rf0 and .

30. Thank you for your attention. Conference on Computational Physics 2006 * This work was supported in part by AFOSR Cathodes and Breakdown MURI04 grant FA9550-04-1-0369, AFOSR STTR Phase II contract FA9550- 04-C-0069, and the Air Force Research Laboratory - Kirtland.

32. MC : E-Field Trace The normal electric field and the number of electrons oscillate with time only for Case 1 in the MC model.

33. MC versus PIC Results Case 1 Like the PIC simulation result, the oscillation period in our MC simulation is half the rf period. However there is still a significant discrepancy in amplitude and phase between the MC and PIC results, which comes from the assumptions on which the MC simulation is based. Like the PIC simulation result, the oscillation period in our MC simulation is half the rf period. However there is still a significant discrepancy in amplitude and phase between the MC and PIC results, which comes from the assumptions on which the MC simulation is based.

34. MC versus PIC Results The parameter regime where the multipactor discharge develops is also the narrower in the MC simulation than in the PIC simulation.

35. PIC : Power Trace Case 1

36. PIC : Power Trace ~ 5% Case 1 In vacuum multipactor discharge, the rf phase randomization of electrons occurs only upon the collision with the surface. The phase delay of the discharge power with respect to the input power comes from the finite transit time for electrons to interact with the surface. It means that the electrons are not totally in equilibrium with the local rf electric field. As the transit time is larger (or the electric field is smaller), the phase difference is larger. In vacuum multipactor discharge, the rf phase randomization of electrons occurs only upon the collision with the surface. The phase delay of the discharge power with respect to the input power comes from the finite transit time for electrons to interact with the surface. It means that the electrons are not totally in equilibrium with the local rf electric field. As the transit time is larger (or the electric field is smaller), the phase difference is larger. ~ 2% ~ 0.5% Case 2

37. PIC : Scaling with E rf0 /f rf The shape of the closed curve of the trajectory depends on the amplitude of the rf electric field normalized to the rf frequency (E rf0 /f rf ). Cases 1 and 4Cases 2 and 3 Decay Grow

38. At transient Strong Weak At the steady state Time At the beginning PIC: Spatial Distribution of Electrons in TE 10 Time X (um) Z (um) X (um)

39.  Susceptibility Curve Center Periphery At transientAt steady state Explanation of Spatial Distribution in TE 10 Discharge on (Positive growth rate)

40. Experiment for the Breakdown on the Air Side (Air)  The HPM surface flashover experiments at Texas Tech Univ. [Ref] G. Edmiston, J. Krile, A. Neuber, J. Dickens, and H. Krompholz, “High Power Microwave Surface Flashover of a Gas-Dielectric Interface at 90 to 760 Torr,” IEEE Trans. Plasma Sci. (to be published). WR284 S-Band waveguide 7.21 cm X 3.40 cm (A = 24.5 cm2)

41. PIC: Discharge Formation Time Discharge formation time  Assuming g : effective volume ionization rate obtained by fitting the number trace t0 : determined from the time that mean kinetic energy reaches steady state, assuming g also reaches steady state.

42. Comparison Flashover time: Experiment at Texas Tech Univ. (Air) 3 MW 3 MW, UV 4.5 MW Discharge formation time: PIC (Argon) Since the statistical delay time is not considered in the simulation and the background gas is different, there is an order of magnitude difference in time between experiment and simulation. But, the qualitative trends are similar. Since the statistical delay time is not considered in the simulation and the background gas is different, there is an order of magnitude difference in time between experiment and simulation. But, the qualitative trends are similar.

43. PIC:2 nd Order Method for Particle Collection  The velocity and position at time the particle crosses the boundary tntn t n+1/2 t n+1 Velocity Position [Ref] H.C. Kim, Y. Feng, and J.P. Verboncoeur, “Algorithms for collection, injection, and loading in particle simulations ”, J. Comput. Phys. (to be published)

44. PIC: 2 nd Order Method for Particle Ejection t n-1 t n-1/2 tntn Velocity Position