Improved design of a high-voltage vacuum-insulator interface

We have conducted a series of experiments designed to measure the flashover strength of various azimuthally symmetric $45°$ vacuum-insulator configurations. The principal objective of the experiments was to identify a configuration with a flashover strength greater than that of the standard design, which consists of a $45°$ polymethyl-methacrylate (PMMA) insulator between flat electrodes. The thickness $d$ and circumference $C$ of the insulators tested were held constant at 4.318 and 95.74 cm, respectively. The peak voltage applied to the insulators ranged from 0.8 to 2.2 MV. The rise time of the voltage pulse was 40–60 ns; the effective pulse width [as defined in Phys. Rev. ST Accel. Beams 7, 070401 (2004)] was on the order of 10 ns. Experiments conducted with flat aluminum electrodes demonstrate that the flashover strength of a crosslinked polystyrene (Rexolite) insulator is $(18\pm 7)\%$ higher than that of PMMA. Experiments conducted with a Rexolite insulator and an anode plug, i.e., an extension of the anode into the insulator, demonstrate that a plug can increase the flashover strength by an additional $(44\pm 11)\%$. The results are consistent with the Anderson model of anode-initiated flashover, and confirm previous measurements. It appears that a Rexolite insulator with an anode plug can, in principle, increase the peak electromagnetic power that can be transmitted across a vacuum interface by a factor of $[(1.18)(1.44){]}^2=2.9$ over that which can be achieved with the standard design.

Figure 1

Idealized 2D $45°$ vacuum-insulator interface. The anode triple junction (atj) is the point at which the vacuum, insulator, and anode regions meet; the cathode triple junction (ctj) is similarly defined.

Figure 2

The absolute value of the electric-field magnitude $E_m$ as a function of position for the idealized $45°$ vacuum-insulator interface outlined in Fig. 1. The calculation assumes that the dielectric constant of the insulator $\epsilon =2.55$. The anode triple junction (atj) is the point at which the vacuum, insulator, and anode regions meet; the cathode triple junction (ctj) is similarly defined. The color legend is a linear scale. The field is given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1.

Figure 3

Electric fields as a function of distance along the vacuum-insulator interface of the idealized $45°$ insulator-electrode system outlined in Figs. 1, 2. The plots assume that the dielectric constant of the insulator $\epsilon =2.55$. The quantity $E_n$ is the absolute value of the electric field normal to the interface, $E_t$ is the absolute value of the field tangent to the interface, and $E_m=(E_n^2+E_t^2{)}^{1/2}$. The fields are given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1. The distance from the ctj is given in units of $2^{1/2}d$, the total length of the interface.

Figure 4

The quantity $v$ as a function of $\epsilon$ for the idealized $45°$ vacuum-insulator system outlined in Figs. 1, 2. The absolute value of the electric-field magnitude $E_m$ near either an anode or cathode triple junction (atj or ctj) is proportional to $r^{v-1}$, where $r$ is the distance from the junction [51, 52].

Figure 5

The absolute value of the electric-field magnitude $E_m$ as a function of distance along the vacuum-insulator interface of the idealized $45°$ system outlined in Figs. 1, 2. The field is that on the vacuum side of the interface, and assumes that the dielectric constant of the insulator $\epsilon =2.55$. The plots compare the field obtained numerically with those given analytically by Eqs. (1, 2, 3). [The numerical result is identical to that labeled $E_m$ (vac) in Fig. 3.] The relation $E_m\propto r^{-0.1401}$ is normalized to the numerical result at a distance $0.01(2^{1/2}d)$ from the anode triple junction; the relation $E_m\propto r^{0.1401}$ is normalized at a distance $0.01(2^{1/2}d)$ from the cathode junction.

Figure 6

The characteristic value of $E_m$ near the anode and cathode triple junctions for the idealized $45°$ vacuum-insulator interface outlined in Figs. 1, 2. Plotted is the field on the vacuum side of the interface as a function of the dielectric constant $\epsilon$. We arbitrarily define the characteristic field to be that at the interface, at a distance $(0.01)2^{1/2}d$ from a junction.

Figure 7

The absolute value of the electric-field magnitude $E_m$ as a function of position for an idealized 2D $45°$ vacuum-insulator interface with a $d/4$ anode plug. The figure assumes that the dielectric constant of the insulator $\epsilon =2.55$. The anode triple junction (atj) is the point at which the vacuum, insulator, and anode regions meet; the cathode triple junction (ctj) is similarly defined. The color legend is a linear scale. The field magnitude is given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1. Comparing Figs. 2, 7, it is clear that the plug decreases significantly the field at the anode triple junction.

Figure 8

The absolute value of the electric-field magnitude $E_m$ on the vacuum side of an idealized 2D $45°$ vacuum-insulator interface, as a function of distance along the interface. The figure assumes that the dielectric constant of the insulator $\epsilon =2.55$. The field is plotted for four different anode-plug depths. [The plot for the case with no plug is identical to that labeled $E_m$ (vac) in Fig. 3.] The field is given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1. The distance from the ctj is given in units of $2^{1/2}d$, which is the total length of the vacuum-insulator interface.

Figure 9

The peak value of $E_m$ on the vacuum side of an idealized 2D $45°$ vacuum-insulator interface, as a function of anode-plug depth. The figure assumes that the dielectric constant of the insulator $\epsilon =2.55$. (When the depth is equal to 0, we plot the characteristic value of $E_m$ near the anode triple junction.) Also plotted is the characteristic value of $E_m$ near the cathode triple junction. The fields are given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1.

Figure 10

Outline of the experimental arrangement. The hardware is cylindrically symmetric about the axis. The outer radius of the insulator is 22.48 cm.

Figure 11

Detail view of Fig. 10. The insulator-electrode geometry shown is that of configurations F, G, and H.

Figure 12

The absolute value of the electric-field magnitude $E_m$ as a function of position for the axisymmetric insulator-electrode configuration of Figs. 10, 11. The field assumes that the dielectric constant of the insulator $\epsilon =2.55$. The color legend is a linear scale. The field is given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1. The field plotted does not include effects due to the O-ring grooves shown in Figs. 10, 11. A calculation with the grooves included shows that they change the peak value of $E_m$ at the vacuum-insulator interface by 1%, and that the field very near the sharp corners of the grooves are on the order of $3V/d$. This assumes that the grooves are completely filled with ethylene propylene ($\epsilon =2.6$), the O-ring material.

Figure 13

The absolute value of the electric-field magnitude $E_m$ on the vacuum side of the vacuum-insulator interface, as a function of distance along the interface, for 6 of the 9 configurations listed in Table . (The fields for configurations C and D are similar to that of B, except that the C and D fields are somewhat lower near the cathode triple junction. The field for configuration E is similar to that of F, G, and H, except that the field for E is somewhat higher near the cathode junction.) The fields are given in units of $V/d$, where $V$ is the voltage across the insulator and $d$ is the insulator thickness as defined by Fig. 1. The distance from the ctj is given in units of $2^{1/2}d$, which is the total length of the vacuum-insulator interface.

Figure 14

Typical voltage pulses applied across an insulator for the flashover experiments.