Langevin simulation of rf collisional multipactor breakdown of gases

The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed.

Figure 1

The model geometry with the lower $\left(P\right)$ and upper $\left(P^{\prime }\right)$ coated surfaces separated by the gap height $D$.

Figure 2

(Color online) The maximum simulation pressures and different microwave peak amplitudes $V_o$ for argon with $N_s=200$.

Figure 3

Structure of the numerical simulations.

Figure 4

(Color online) The predicted rf breakdown voltage thresholds corresponding to the experiments of Ref. [17] for different gas pressures. The decimal logarithm is used in both axes.

Figure 5

(Color online) The rf voltage thresholds as a function of $f_{w}D$ for the low pressure electron multipactor. The decimal logarithm is employed in both axes.

Figure 6

(Color online) The rf voltage thresholds for rf breakdown in argon as a function of $f_{w}D$ for different values of the ratio ${\nu }_m/f_w$ within the collisional multipactor plasma range of pressures. The decimal logarithm is employed in all axes.

Figure 7

(Color online) The rf voltage thresholds for rf breakdown as a function of $f_{w}D$ for large values of the ratio ${\nu }_m/f_w$. The decimal logarithm is employed in both axes.