Different approach to pulsed high-voltage vacuum-insulation design

A theoretical methodology promising improved design of vacuum insulation in high-voltage pulsed-power systems is described. It consists of shaping the electromagnetic fields within the system in such a way that charged particles which can in principle initiate vacuum surface breakdown are deflected away from the insulator surface, and secondary electrons, if emitted, are prevented from restriking the surface. Thus, vacuum surface breakdown is prevented before it is able to develop. Our methodology is presented here by a set of case studies.

Figure 1

Equipotential curves and electron trajectories (rays from left to right) in vacuum in a half cross section of a coned axially symmetric insulator ring (olive colored). The potential is applied between two parallel plates attached to the ends $z=0$ and 10 cm of the drawn device. Cone angles are $3.8°$ [in (a) and (c)], $45°$ [in (b) and (d)], $⟨E_Z⟩=100\mathrm{kV}/\mathrm{cm}$ and ${\epsilon }_r=3$. In (a) and (b), ray traced trajectories of electrons emitted on the cathode surface near the triple junction are drawn. In (c) and (d), trajectories of electrons originating on the surface of the insulator are shown.

Figure 2

$E_{\parallel }$ (dashed) and $E_{\perp }$ (full) along a line $100\mu \mathrm{m}$ away from the insulator surface in vacuum for the system in Fig. 1 with an anode-cathode separation of 10 cm, 1 V applied voltage, and ${\epsilon }_r=3$ for three cone angles.

Figure 3

Half cross section of an axially symmetric stacked-ring insulator between the parallel cathode (left gray end surface) and anode (right gray end surface). All gray surfaces are conductors, olive colored surfaces are insulators (${\epsilon }_r=3$), and the yellow area is filled with insulating oil (${\epsilon }_r=2.7$). Electrons (blue trajectories) flow from left to right. In (a) electrons are emitted on the cathode surface. In (b) the trajectories of all possible secondary electrons emitted along the surfaces of the stack are calculated and drawn. The lines almost parallel to the side plates are calculated equipotential curves for 1 MV applied voltage.

Figure 4

Equipotential curves at the front end of a typical pulsed-power machine (half cross section of the axially symmetric structure is drawn). Low current electrons are emitted at two “weak” points: at the cathode triple junction and along the central stalk. Parts are colored as in Fig. 3.

Figure 5

Same as Fig. 4 but the insulator is replaced by a stack.

Figure 6

TRAK [14, 15] ray-tracing calculation of the space charge limited emission from the central stalk of the device of Fig. 5. Contours of the beam generated $B_{\theta }$ are also drawn. 2.4 MV is applied and the total current obtained is 44 kA.

Figure 7

The trajectories of the electrons shown in Fig. 5 in the presence of the beam generated magnetic and electric fields as calculated in Fig. 6.

Figure 8

Part (a) is the same as Fig. 6 for a monolithic insulator and part (b) the same as Fig. 7 for the electrons shown in Fig. 4.

Figure 9

The voltage vs time (a) as measured at various locations during the PIC calculation performed on the system shown in (b). The geometry of the PIC calculations in 9b is the same as that in Fig. 4.

Figure 10

PIC calculated phase space of all electrons at $t=7.003$ (a), 9.664 (b), 45.007 (c) nsec for the system of Fig. 9b. In (d) charge density contours are drawn for the same instant as the phase space in (c).

Figure 11

Same as Fig. 10 with a stack replacing the monolithic insulator for $t=6.502$ (a), 9.211 (b), 45.602 (c) nsec, and charge density contours in (d) at 45.062 nsec.

Figure 12

Ray-tracing calculations at the front of a pulsed-power machine with a central stalk. The knob in the cathode field-shaping ring (CFSR) and the notch in the anode field-shaping ring (AFSR) are simple attempts to add mechanical strength but have a negligible EM effect. In (a) electrons (blue trajectories) originating on the cathode surfaces, in (b) secondaries emitted along the monolithic insulator, whereas in (c) positive ions (red trajectories) emitted at the enlarged anode end are traced. Contours of the voltage distribution are also drawn.

Figure 13

Values of the components of the electric field with 2.2 MV applied voltage $10\mu \mathrm{m}$ below the monolithic insulator in Fig. 12 vs $z$.

Figure 14

Space charge limited emission of an electron beam current from the cathode stalk in (a) generates magnetic and electric fields. In (b) the low current electrons originating on the cathode field-shaping ring and the central stalk are propagated in the presence of the fields generated in (a). In (c) secondaries of the type shown in 12b are traced in the presence of these fields.

Figure 15

Same as Fig. 9a, for the geometry of Fig. 14.

Figure 16

PIC calculated phase space of all electrons at $t=10.379$ (a), 12.995 (b), 17.552 (c), and 45.062 (d) nsec for the system of Fig. 14. In (e) the charge density contours are drawn at the same time instant as in (d).

Figure 17

Ray traced secondary electrons emitted from surfaces near the cathode triple junction for (a) collinear surfaces, (b) with the conducting ring protruding 0.1 mm into the vacuum above the insulator surface, and (c) with the conducting ring recessed 0.1 mm beneath the insulator surface. $M$, $I$, and $V$ designate regions of conducting material, insulator, and vacuum, respectively. ${\epsilon }_r=2.7$. The colors represent contours of fixed potential and the applied voltage was 2000 kV over a device length of 10 cm, that is $⟨E_z⟩=200\mathrm{kV}/\mathrm{cm}$. Electron trajectories move away from the surfaces into the vacuum.

Figure 18

Same as Fig. 17 but with the conductor-insulator interface coned to $45°$.

Figure 19

Same as Figs. 17, 18 but for the anode field-shaping ring. Positive ion trajectories are drawn as red curves in the vacuum.

Figure 20

Ray traced electrons emitted on the cathode surface near an imperfect triple junction. In (a) an ordinary cathode triple junction is studied whereas in (b) an imperfect flat cathode triple junction of the perfect type seen in Fig. 17a. The imperfections are introduced by rounding specific corners to a radius of 0.1 mm. All other parameters are the same as in Fig. 17.