Abstract
Multipactor breakdown in a single waveguide iris is analyzed using the quasistatic approximation for the spatial distribution of the rf field in the iris. Based on the conformal mapping approach, an analytical description is given of the rf field structure in the iris. It is shown that in the central part of any iris with a length to height ratio greater than approximately 0.5, the rf field structure is close to that between two parallel plates. The multipactor threshold for the iris is determined mainly by electron losses from the central part of the iris where the losses are due to the tangential component of the emission velocity of secondary electrons. The effective length of the iris central part is determined and an estimate of the multipactor threshold for the iris is found in terms of the conventional parameters: Applied rf voltage, product of rf frequency and iris height, and iris length to height ratio. Numerical simulations are also carried out using the exact analytical description of the quasistatic rf field and taking into account a spread of electron emission velocities.
This work was partially supported by INTAS under Grant No. 0610000249098 and by the Russian Foundation for Basic Research through Grant No. 060216455a.
I. INTRODUCTION
II. CONFORMAL MAPPING ANALYSIS OF THE IRIS GEOMETRY
III. EQUATIONS OF ELECTRON MOTION WITHIN THE CONFORMAL MAPPING APPROACH
IV. NUMERICAL SIMULATIONS OF THE MULTIPACTOR INSIDE A 2D IRIS
V. CONCLUSION
Key Topics
 Electric fields
 17.0
 Laplace equations
 8.0
 Secondary emission
 8.0
 Equations of motion
 7.0
 Spatial analysis
 7.0
Figures
The 2D model used in the conformal mapping analysis.
The 2D model used in the conformal mapping analysis.
Illustration of the transformation given by Eq. (4). The lines ABCD and EFGH show the position of the iris metal surfaces in the plane (left) and in the plane (right).
Illustration of the transformation given by Eq. (4). The lines ABCD and EFGH show the position of the iris metal surfaces in the plane (left) and in the plane (right).
The variation of the ratio for small values of the parameter . Solid line represents the approximation given by Eq. (9) and ∗ denotes the result of full numerical calculations.
The variation of the ratio for small values of the parameter . Solid line represents the approximation given by Eq. (9) and ∗ denotes the result of full numerical calculations.
The variation of the function with the parameter . Solid line represents the approximation given by Eq. (9) and ∗ denotes the result of full numerical calculations.
The variation of the function with the parameter . Solid line represents the approximation given by Eq. (9) and ∗ denotes the result of full numerical calculations.
The dependence of the normalized electric field strength, , on normalized coordinate along the central field line for different length to height ratios (full numerical solution).
The dependence of the normalized electric field strength, , on normalized coordinate along the central field line for different length to height ratios (full numerical solution).
The dependence of the normalized electric field strength, , on normalized coordinate along the upper iris boundary for different length to height ratios (full numerical solution).
The dependence of the normalized electric field strength, , on normalized coordinate along the upper iris boundary for different length to height ratios (full numerical solution).
The evolution of the average number of electrons, (time is normalized to half the rf period), calculated for the planeparallel model (+), the model of an iris with uniform rf field and the true geometrical length, i.e., (▵), the model of an iris with uniform rf field and the effective length (○), and the exact 2D model of the iris (●). The parameters of the secondary electron emission are and (the latter parameters correspond to a first crossover energy of for the secondary emission yield, which was used previously in Ref. 7 and coincides with the work function Wf2 given in Table A6 to construct the multipactor charts for silver). The frequency , rf voltage amplitude , iris height , and initial electron energy are chosen so to realize the first order resonance and maximum secondary emission yield within the planeparallel model. The iris length to height ratio is . The number of calculated electron trajectories is taken to be .
The evolution of the average number of electrons, (time is normalized to half the rf period), calculated for the planeparallel model (+), the model of an iris with uniform rf field and the true geometrical length, i.e., (▵), the model of an iris with uniform rf field and the effective length (○), and the exact 2D model of the iris (●). The parameters of the secondary electron emission are and (the latter parameters correspond to a first crossover energy of for the secondary emission yield, which was used previously in Ref. 7 and coincides with the work function Wf2 given in Table A6 to construct the multipactor charts for silver). The frequency , rf voltage amplitude , iris height , and initial electron energy are chosen so to realize the first order resonance and maximum secondary emission yield within the planeparallel model. The iris length to height ratio is . The number of calculated electron trajectories is taken to be .
The multipactor threshold as a function of the height to length ratio . The predictions, based on the approximation of a uniform rf field and an effective iris length, , are shown by dashed lines, whereas circles represent results of the exact numerical calculations. For comparison, measurement data from Ref. 6 are also included (+). The parameters used in the calculations: Height , rf frequency , and electron initial energy , and for the secondary emission properties, and (the latter parameters correspond to a first crossover energy of for the secondary emission yield in accordance with the work function Wf2 given in Table A6 for silver used in Ref. 7).
The multipactor threshold as a function of the height to length ratio . The predictions, based on the approximation of a uniform rf field and an effective iris length, , are shown by dashed lines, whereas circles represent results of the exact numerical calculations. For comparison, measurement data from Ref. 6 are also included (+). The parameters used in the calculations: Height , rf frequency , and electron initial energy , and for the secondary emission properties, and (the latter parameters correspond to a first crossover energy of for the secondary emission yield in accordance with the work function Wf2 given in Table A6 for silver used in Ref. 7).
Illustration of the multipactor growth for different rf voltages applied to irises with the same height, , but with different lengths. The parameters used in the simulations are rf frequency , electron initial energy , and for the secondary emission properties, and . In each figure, the relative electron number, , after some particular time, , is shown as a function of the voltage amplitude, (in Volts). The arrows indicate peaks corresponding to multipactor resonances of order indicated by numbers (1, 3, 5). The peak indicated by the letter h here designates the hybrid multipactor resonances (Ref. 15). The iris length, (in mm) and the simulation time, (in rf periods), are shown in each particular figure.
Illustration of the multipactor growth for different rf voltages applied to irises with the same height, , but with different lengths. The parameters used in the simulations are rf frequency , electron initial energy , and for the secondary emission properties, and . In each figure, the relative electron number, , after some particular time, , is shown as a function of the voltage amplitude, (in Volts). The arrows indicate peaks corresponding to multipactor resonances of order indicated by numbers (1, 3, 5). The peak indicated by the letter h here designates the hybrid multipactor resonances (Ref. 15). The iris length, (in mm) and the simulation time, (in rf periods), are shown in each particular figure.
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