CCP 2006 (S05-I22: Invited Talk) Modeling of RF Window Breakdown Transition of window breakdown from vacuum multipactor discharge to rf plasma 2006. 08. 29 H. C. Kim, Y. Chen, and J. P. Verboncoeur Dept. of Nuclear Engineering, UC Berkeley
Topic 0. • 0. Introduction and Models • I. Vacuum Multipactor Discharge • II. Transition to RF Plasma
y x z Undesirable Discharge in HPMs (High-Power Microwave) Conductor RF Window (Dielectric) RF generator (e.g. Magnetrons, Linear beam tubes, Gyrotrons, Free-Electron Lasers, and so on) Either Vacuum or Background Gas Incoming EM wave > Outgoing EM wave • Discharge can degrade device performance or even damage devices, including catastrophic window failure. z : direction of wave propagation
In Vacuum (Multipactor Discharge) (TE or TEMmode) • Single-surface multipactor on a dielectric • Multipactor discharge* is an avalanche caused by secondary electron emission. Vacuum + + + + + - - : leads to electron energy gain. - (= life time) - - (maximum distance) : makes electrons return to the surface. * Observed in various systems (e.g. RF windows, accelerator structures, microwave tubes and devices, and rf satellite payloads)
Analytic Solution of Single Particle Motion • Solution of the equation of motion for the electron in Vacuum (TE or TEMmode) For the constant Ez = Ez0 during the flight, vx,0, vy,0: initial velocity of the electron emitted from the surface 0: initial phase of the rf electric field at that time (t=t0) - - • The z- and y-components of the impact electron energy
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. - + + - - + - + + - +
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 probabilistic event - + - - • 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.
Secondary Emission due to Electron Impact • Energy and angular dependence of secondary emission yield (the ratio of the incident flux to the emission flux) - i, i, (Electron Impact Energy) [Ref] Vaughan et al, IEEE (1989); IEEE (1993) (Electron Impact Angle)
1D3V Particle-In-Cell (PIC) Model x • Condition of • left dielectric + + + + + + + + + - y + - + - - Dielectric Dielectric (δ=0) - - - - + + - L • Simulation Tool : Modified XPDP1 from PTSG, UC Berkeley [Ref] J.P. Verboncoeur et al., J. Comput. Phys. 104, 321 (1993)
Topic I. • 0. Introduction and Models • I. Vacuum Multipactor Discharge • II. Transition to RF Plasma * Our model is based on electrostatic fields and the magnetic field is not taken into account.
Dynamics using Monte-Carlo Simulation* • Susceptibility Curve for Plane Wave Discharge on (Positive growth rate) • Discharge off : low due to • Too high impact energy • Too small impact energy Problem: No oscillation appears even though * [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998)
Model of Monte-Carlo Simulation • Emission of initial seed electrons from the surface vz,0, vy,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) • Update • Ejection of multiple secondary electrons (Nn+1) from the surface vz,0, vy,0: (from the energy distribution of secondary electrons) : The phase of next injection is taken from the phase of impact for the parent electron. * [Ref] Ang et al, IEEE Trans. Plasma Sci. 26, 290 (1998)
Dynamics using PIC Simulation (solving field eqn. self-consistently) • PIC simulation shows that the electron number and the Ez oscillate at twice the rf frequency, saturating after 1 ns. • Ez oscillates in and out of the susceptibility region. [Ref] H.C. Kim and J.P. Verboncoeur, Phys. Plasmas 12, 123504 (2005) Plane Wave
PIC: Susceptibility Curve (Plane vs. TE10) • Effect of transverse field structure Plane wave TE10 mode ~ x 1.5 TE10mode z : direction of wave propagation • In TE10 mode, the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant.
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 TE10,the upper boundary of the susceptibility diagram is nearly vertical so that only the lower boundary is relevant.
Topic II. • 0. Introduction and Models • I. Vacuum Multipactor Discharge • II. Transition to RF Plasma
Collision with Argon Background Gas • The argon gas is used in this study because of its simplicity in the chemistry (compared with air). • Electron-Neutral Collision • Ion-Neutral Collision
PIC: Number of Particles (I) • Vacuum multipactor discharge • The secondary electron emission is the only mechanism for generating electrons. • 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
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.
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.
PIC: Electron Energy Distribution Spatially averaged • 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.
PIC: Electron and Ion Densities • 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. * Time-averaged over a cycle
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.
PIC: Secondary Electron Emission • Secondary electron emission yield on the dielectric Transition Pressure (10~50 Torr) EEPF of rf plasma is Druyvesteyn. surface discharge is collisionless. • 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. * For particles accumulated over a cycle
Experiment for the Breakdown on the Air Side • The HPM surface flashover experiments at Texas Tech Univ. Incident P Transmitted P Reflected P Absorbed P = Incident P – Transmitted P – Reflected P Flashover delay time [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).
Experiment for the Breakdown on the Air Side Air: 90 ~ 760 Torr 3 MW, UV 3 MW 4.5 MW f = 2.85 GHz Simple theory : L. Gould and L. W. Roberts, J. Appl. Phys. 27, 1162 (1956). • is universal for different Erf0 at the given pressure range.
PIC: Discharge Formation Time (I) • Simulation results of argon gas for various E-fields and frequencies • At very low pressures • At very high pressures, • is universal for different Erf0 and .
PIC: Discharge Formation Time (II) • Simulation results of argon gas for various E-fields and frequencies [ns] • At low pressures, • is universal for different Erf0 and .
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 Erf0 and .
Conference on Computational Physics 2006 Thank you for your attention. * 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.
MC : E-Field Trace • The normal electric field and the number of electrons oscillate with time only for Case 1 in the MC model.
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.
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.
PIC : Power Trace Case 1
PIC : Power Trace ~ 0.5% ~ 2% Case 2 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. ~ 5%
PIC : Scaling with Erf0/frf Grow Decay Cases 1 and 4 Cases 2 and 3 • The shape of the closed curve of the trajectory depends on the amplitude of the rf electric field normalized to the rf frequency(Erf0/frf).
PIC: Spatial Distribution of Electrons in TE10 X (um) X (um) At the beginning At transient Time Z (um) Z (um) Weak Time Strong X (um) At the steady state Weak Z (um)
Explanation of Spatial Distribution in TE10 • Susceptibility Curve Center Discharge on (Positive growth rate) Periphery At transient At steady state
Experiment for the Breakdown on the Air Side • The HPM surface flashover experiments at Texas Tech Univ. • WR284 S-Band waveguide • 7.21 cm X 3.40 cm • (A = 24.5 cm2) (Air) [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).
PIC: Discharge Formation Time Assuming • Discharge formation time 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.
Comparison • Flashover time: Experiment • at Texas Tech Univ. (Air) • Discharge formation time: PIC (Argon) 3 MW, UV 3 MW 4.5 MW • 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.
PIC:2nd Order Method for Particle Collection • The velocity and position at time the particle crosses the boundary Velocity tn+1/2 [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) tn+1 tn Position
PIC: 2nd Order Method for Particle Ejection Velocity tn-1/2 tn tn-1 Position