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Figure from:Physics and modeling of an end-Hall (gridless) ion source

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FIG. 12. Distribution of the electron current density across an element of magnetic field line (the electron current density is integrated in the azimuthal direction) (a) in the simulation domain. (b) Zoom representation of a region close to the source.

Figure 12 Distribution of the electron current density across an element of magnetic field line (the electron current density is integrated in the azimuthal direction) (a) in the simulation domain. (b) Zoom representation of a region close to the source.

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FIG. 1. Geometry of the end-Hall ion source. The cathode is an electron emitting filament. Some of the emitted electrons are used to neutralize the ion beam, and the rest are accelerated to the anode. The back plate is floating.
FIG. 1. Geometry of the end-Hall ion source. The cathode is an electron emitting filament. Some of the emitted electrons are used to neutralize the ion beam, and the rest are accelerated to the anode. The back plate is floating.
FIG. 2. Simulation domain showing the cylindrical (x,r) grid used for heavy particle transport and the magnetic field lines grid used for electron transport. where x and r are the axial and radial position coordinates. This stream function 4 is constant along the magnetic field
FIG. 2. Simulation domain showing the cylindrical (x,r) grid used for heavy particle transport and the magnetic field lines grid used for electron transport. where x and r are the axial and radial position coordinates. This stream function 4 is constant along the magnetic field
FIG. 3. (Color online) Schematic of the different currents in the source. The directions indicated by the arrows correspond to the charged particle fluxes (thus the negative signs for the corresponding electron currents). The sign conventions are such that the discharge current J, is defined by —1qg=Tee ten = Tea + Tig. The meaning of the different currents is discussed in the text. To better understand the operation of the EH source, it is useful to look closely at the different currents flowing in the device. The scheme of Fig. 3 shows these different cur- rents. In this paper, we assume that the discharge current J, is equal to the current emitted by the cathode J. + Jen, where Te, is the part of the cathode emitted electron current used for beam neutralization (/., = —Jip; Jip is the ion beam current) and /., corresponds to electrons emitted by the cathode, accelerated in the electric field between the cathode and the anode and providing ionization. We choose the signs of the currents such that —/g = J, + Jen, where Jj is the discharge current. In the simulations presented here, no net current is
FIG. 3. (Color online) Schematic of the different currents in the source. The directions indicated by the arrows correspond to the charged particle fluxes (thus the negative signs for the corresponding electron currents). The sign conventions are such that the discharge current J, is defined by —1qg=Tee ten = Tea + Tig. The meaning of the different currents is discussed in the text. To better understand the operation of the EH source, it is useful to look closely at the different currents flowing in the device. The scheme of Fig. 3 shows these different cur- rents. In this paper, we assume that the discharge current J, is equal to the current emitted by the cathode J. + Jen, where Te, is the part of the cathode emitted electron current used for beam neutralization (/., = —Jip; Jip is the ion beam current) and /., corresponds to electrons emitted by the cathode, accelerated in the electric field between the cathode and the anode and providing ionization. We choose the signs of the currents such that —/g = J, + Jen, where Jj is the discharge current. In the simulations presented here, no net current is
FIG. 4. (Color online) Magnetic field lines (contours) and intensity of the B field (gray shading). The maximum B field is 80 mT. Three values have been considered for the maximum B field in the simulations: 80, 60, and 40 mT.
FIG. 4. (Color online) Magnetic field lines (contours) and intensity of the B field (gray shading). The maximum B field is 80 mT. Three values have been considered for the maximum B field in the simulations: 80, 60, and 40 mT.
FIG. 5. (Color online) Electric potential distribution for a discharge current of 1 A, an argon mass flow rate of 0.50 mg/s, and a background pressure of 8.4 mPa. The magnetic field distribution is represented in Fig. 4 (maximum field 80 mT). Two ion trajectories are also represented. The dashed line indi- cates the position of the cathode filament.
FIG. 5. (Color online) Electric potential distribution for a discharge current of 1 A, an argon mass flow rate of 0.50 mg/s, and a background pressure of 8.4 mPa. The magnetic field distribution is represented in Fig. 4 (maximum field 80 mT). Two ion trajectories are also represented. The dashed line indi- cates the position of the cathode filament.
FIG. 8. Space distribution of the argon atom density in units of 10'° m™? in the same conditions as in Fig. 5.
FIG. 8. Space distribution of the argon atom density in units of 10'° m™? in the same conditions as in Fig. 5.
1 FIG. 7. Distribution of the ionization rate in units of 10°? m~*s~! in the same conditions as in Fig. 5.
1 FIG. 7. Distribution of the ionization rate in units of 10°? m~*s~! in the same conditions as in Fig. 5.
FIG. 9. Distribution of the plasma density in units of 10'* m~ (a) ona large scale and (b) in the anode region in the same conditions as in Fig. 5.
FIG. 9. Distribution of the plasma density in units of 10'* m~ (a) ona large scale and (b) in the anode region in the same conditions as in Fig. 5.
FIG. 10. (Color online) Equipotential contours (gray shading) and magnetic field lines in the same conditions as in Fig. 5.
FIG. 10. (Color online) Equipotential contours (gray shading) and magnetic field lines in the same conditions as in Fig. 5.
FIG. 11. Space distribution of the electron mean energy in the same condi- tions as in Fig. 5.
FIG. 11. Space distribution of the electron mean energy in the same condi- tions as in Fig. 5.
FIG. 14. (Color online) Calculated ion currents as a function of the argon mass flow rate for different values of the discharge current (triangles: 0.5 A; squares: | A; circles: 1.5 A). The solid symbols correspond to the ion beam current, and the open symbols represent the total ion production (i.e., ion beam current plus ion currents to the anode and to the back plate). The line labeled J/g, corresponds to the current equivalent to full ionization of the ar- gon mass flow rate (full ionization of an argon flow of | mg/s corresponds to a current of 2.4 A).
FIG. 14. (Color online) Calculated ion currents as a function of the argon mass flow rate for different values of the discharge current (triangles: 0.5 A; squares: | A; circles: 1.5 A). The solid symbols correspond to the ion beam current, and the open symbols represent the total ion production (i.e., ion beam current plus ion currents to the anode and to the back plate). The line labeled J/g, corresponds to the current equivalent to full ionization of the ar- gon mass flow rate (full ionization of an argon flow of | mg/s corresponds to a current of 2.4 A).
FIG. 13. Space distribution of (a) electron-neutral and (b) electron-ion colli- sion frequencies.
FIG. 13. Space distribution of (a) electron-neutral and (b) electron-ion colli- sion frequencies.
FIG. 16. (Color online) Discharge and ion beam current as a function of applied voltage for a constant mass flow rate of 0.55 mg/s (bottom panel). The ratio /,/Iz of ion beam to discharge current as a function of discharge voltage is shown in the top panel. Figure 16 shows the discharge and ion beam currents as a function of applied voltage for a constant mass flow rate. The discharge and beam currents increase monotonously
FIG. 16. (Color online) Discharge and ion beam current as a function of applied voltage for a constant mass flow rate of 0.55 mg/s (bottom panel). The ratio /,/Iz of ion beam to discharge current as a function of discharge voltage is shown in the top panel. Figure 16 shows the discharge and ion beam currents as a function of applied voltage for a constant mass flow rate. The discharge and beam currents increase monotonously
FIG. 15. (Color online) Calculated discharge voltage as a function of the ar- gon mass flow rate for three different values of the discharge current: 0.5, | A, and 1.5 A (solid symbols). The solid symbols correspond to the magnetic field of Fig. 4 with a maximum of 80 mT used for all results presented in this paper. The open triangle symbols correspond to a discharge current of | A with the same distribution of magnetic field, but with a maximum mag- netic field of 60 mT (arrow to the left) or 40 mT (arrow to the right).
FIG. 15. (Color online) Calculated discharge voltage as a function of the ar- gon mass flow rate for three different values of the discharge current: 0.5, | A, and 1.5 A (solid symbols). The solid symbols correspond to the magnetic field of Fig. 4 with a maximum of 80 mT used for all results presented in this paper. The open triangle symbols correspond to a discharge current of | A with the same distribution of magnetic field, but with a maximum mag- netic field of 60 mT (arrow to the left) or 40 mT (arrow to the right).
FIG. 17. (Color online) Energy distributions of the ion current density (a) integrated over the exhaust plane and (b) at two locations 15 cm away from the back plate, on axis, and off axis at an angle of 20° relative to the dis- charge axis.
FIG. 17. (Color online) Energy distributions of the ion current density (a) integrated over the exhaust plane and (b) at two locations 15 cm away from the back plate, on axis, and off axis at an angle of 20° relative to the dis- charge axis.