Density and potential profiles of non-neutral electron plasmas in a magnetic mirror field

Low-energy non-neutral electron plasmas were confined with an electrostatic potential and a magnetic mirror field of the mirror ratio up to 5. Using a conventional phosphor screen and the unique multiring trap, both radial and axial density profiles of plasmas were measured. With the present experimental parameters, it was confirmed that a plasma density increased at higher field with an electrostatic confinement and that it decreased at higher field with a magnetic mirror confinement. The electrostatic potentials along the magnetic field were estimated with computer simulations.

Figure 1

(a) The basic configuration of an applied magnetic field and electrostatic potential. Open circles denote the measured magnetic field strength on the axis of symmetry when $I_L=10\text{A}$ and $I_H=80\text{A}$. Thin solid line corresponds to the applied electrostatic potential. Arrows show the positions of an electron gun and a phosphor screen. (b) A schematic drawing of the experimental setup.

Figure 2

(Color) Examples of obtained images, radial density profiles, and axial distributions when $R\sim 3$. (a) Image for the electrostatic confinement. (b) Image for the magnetic mirror confinement with a hollow profile. (c) Image for the magnetic mirror confinement with a bell-shaped profile. White dashed lines show the area of the phosphor screen. (d)–(f) show cross sections of corresponding images. Each color represents a different axial position where $V_{cut}$ was applied. (g)–(i) show normalized intensity $I_n\left(z\right)$ along the axis of symmetry.

Figure 3

(Color) Normalized axial intensity distributions with various $R$ for (a) electrostatic confinement and (b) magnetic mirror confinement, respectively. It is seen that the axial distribution becomes linear for the uniform magnetic field $\left(R\sim 1\right)$. (c) Normalized axial electron densities near the axis of symmetry are evaluated with the measured magnetic field strength and plotted as a function of position.

Figure 4

(Color) Calculated density and potential distributions of plasmas with the magnetic mirror field $R\sim 3$. (a) The density distribution in the electrostatic confinement with $r_0=2\text{cm}$ has a higher density at high field. (b) In the magnetic mirror confinement with $r_0=2\text{cm}$, a hollow profile is observed with the higher density at low field. (c) With a smaller radius of $r_0=1\text{cm}$ in the magnetic mirror confinement, a bell-shaped profile is reproduced. Electrostatic potentials corresponding to (a), (b), and (c) are shown in (d), (e), and (f), respectively

Figure 5

(Color) (a) A density distribution during the simultaneous ramping of the magnetic mirror field and grounding of the potential $V_H$. (b) A density distribution in the magnetic mirror confinement with $R\sim 3$ obtained with the simultaneous ramping process. Compared to Fig. 4b, the density distribution is closer to a bell-shaped one.

Figure 6

(Color) (a) Calculated density distributions along the axis of symmetry. Dash-dotted lines are the distributions in a uniform magnetic field at the beginning of simulation. (b) Normalized density distributions along the axis of symmetry, which should be compared to those in Fig. 3c. (c) Electrostatic potentials along the axis of symmetry. It is seen that $\Delta \varphi$ in magnetic mirror confinement (dashed lines) are larger than those in electrostatic confinement (solid lines).