Method of controlling the cyclotron motion of electron beams with a nonadiabatic magnetic field

This paper describes a method for reducing the energy of the cyclotron motion for charged particles in coherent beams using a nonadiabatic magnetic field. For the purpose of reducing the cyclotron motion, a local magnetic field reduction of the main guiding field should be situated in the region of the descending phase of the beam oscillation. The required local magnetic field depression can be produced with a soft iron ring or with a magnet coil. The nonadiabatic element can be positioned on the descending part of any period of the beam oscillation where the beam still remains sufficiently coherent. The effect of reducing the cyclotron motion with such nonadiabatic magnetic field is independent of the electric field of the cathode-anode gap and seems to be a universal method for the cyclotron motion control in coherent beams. Therefore, it can be used for reducing the cyclotron motion of electron beams produced with different kinds of guns with different perveances and sizes. For instance, the method is capable of creating ripple-free, laminar beams even for magneto-immersed guns positioned in a magnetic field of only a few hundred Gs and with a cathode emission current density exceeding $30\mathrm{A}/{\mathrm{cm}}^2$. It can also be applied for guns producing tubular beams, as demonstrated by our simulations. The results of computer simulations are presented, which demonstrate the capability of effective cyclotron motion control with nonadiabatic magnetic field.

Figure 1

Electrostatic models of simulated electron guns: (a) Pierce-type gun and (b) gun with anode overlapping the cathode. The sketches show the profile of the cylindrically symmetric simulation geometries.

Figure 2

Electron beam transmission for $I_{\mathrm{el}}=0.7\mathrm{A}$ and $E_{\mathrm{el}}=8.5\mathrm{kV}$. The electron gun has Pierce geometry with flat cathode, cathode radius $r_{\text{cath}}=1.0\mathrm{mm}$ and the emission current density is $j_{em}=22.3\mathrm{A}/{\mathrm{cm}}^2$. (a) No NA element present and a uniform magnetic field $B=500\mathrm{Gs}$. (b) Iron ring with optimized geometry positioned on the descending phase of the cyclotron motion. The axial distribution of the magnetic field on the beam axis is presented on this plot with the scale on the right.

Figure 3

Cancellation of the cyclotron motion for a beam using a NA coil; $I_{\mathrm{el}}=0.7\mathrm{A}$, $E_{\text{el}}=6.0\mathrm{kV}$, $r_{\text{cath}}=1.0\mathrm{mm}$, $B=1.0\mathrm{kGs}$, and ${\mathrm{IN}}_{\text{coil}}=850$ Amp-turns (IN—product of coil current I and number of turns N).

Figure 4

Effect of a NA magnetic field on the cyclotron motion for a NA coil positioned on the descending part of the third period of cyclotron oscillation: $I_{\mathrm{el}}=0.7\mathrm{A}$, $E_{\mathrm{el}}=6\mathrm{keV}$, $r_{\mathrm{cath}}=1\mathrm{mm}$, and $B=1000\mathrm{Gs}$.

Figure 5

Excitation of the laminar electron beam with a NA iron ring. $I_{\mathrm{el}}=0.7\mathrm{A}$, $E_{\mathrm{el}}=6.0\mathrm{keV}$, $r_{\text{cath}}=1.0\mathrm{mm}$, and $B=1.0\mathrm{kGs}$.

Figure 6

Injection of the electron beam formed with NA element (iron ring) into a raising magnetic field of the guiding solenoid. $I_{\mathrm{el}}=0.7\mathrm{A}$, $E_{\mathrm{el}}=10\mathrm{keV}$, $B_{\mathrm{cath}}=460\mathrm{Gs}$, and $B_{\text{final}}=17000\mathrm{Gs}$.

Figure 7

Hollow electron beam simulation with a NA coil; $I_{\mathrm{el}}=10.0\mathrm{A}$, $E_{\mathrm{el}}=13.7\mathrm{keV}$, and $B_{\mathrm{cath}}=480\mathrm{Gs}$.

Figure 8

Sensitivity of relative beam oscillation $dr/r$ on the current in the NA coil (a) and on its axial position (b). The gun and the electron beam parameters are outlined in Fig. 3. The tracking results (black solid) are shown alongside a semitheoretical prediction (red dashed) which is based on an evaluation of the tracking results in a single arbitrary plane downstream of the NA field.

Figure 9

Transverse motion of the outermost beam electron for the geometry similar to the one presented in Fig. 3. The blue dotted line is for optimized current in the NA coil (860 Amp-turns), the red dashed line for insufficient current in the coil (700 Amp-turns), the green dash-dotted line is for excessive current in the coil (1000 Amp-turns), and the black solid line is for zero current in the NA coil. Initially, the particles move counterclockwise. The black circles mark the points where the beams are traversing the minimum of the NA field modulation.