Lecture 6: High Voltage Gas Switches

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Willis Johns
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1 Lecture 6: High Voltage Gas Switches Switching is a central problem in high voltage pulse generation. We need fast switches to generate pulses, but in our case, they must also hold off high voltages before closing. Gas filled switches are most commonly used. Gas filled switch basic geometry + gas initially acts as insulator between two metal electrodes + switch closes when gas "breaks down", or converts to conducting plasma Gas switching triggering (for timing) + self-breakdown: no timing, Paschen breakdown + electrical: field in switch perturbed by a quickly charged metal electrode + laser or electron beam: laser or beam ionizes gas, an avalanche occurs leading to breakdown Collisions + Charged particle collisions, leading to gas ionization and formation of a conductive channel, are the key to breakdown + Elastic collisions in the conductive channel result in switch resistivity + Cross sections are the fundamental parameter of collisions + A cross section is the effective cross sectional area of a gas particle relative to a particular type of collision + The cross section determines the probability that a single charged particle (usually an electron in the switching case) will interact with a background particle (usually a gas atom or molecule). + The interaction could be ionization of the gas atom or molecule, or elastic or inelastic scattering of the electron

2 Say a beam of particles uniformly interacts with a slab of material total area - A background particle area - sigma N background particles in the slab, total area of background particles slab thickness Probability a beam particle interacts with a background particle background particle density The number of beam particles that interact (assume lost from beam so sign of change in I is negative)

3 change with respect to time sigma, in units of square meters, is the cross section

4 Townsend Breakdown + Model for gas breakdown + electron gains energy from an electric field + electron collides with a background gas atom or molecule + gain: electron ionizes gas, get two electrons and one ion + loss: electron recombines with ion, electron diffuses out, electron is attached by an atom or molecule. Assume electron produces alpha new electron ion pairs per unit length first Townsend coefficient, sigma_i is the electron impact ionization cross section + Current increases exponentially with distance the electrons travel + Ions collected at negative electrode - these can generate new secondary electrons on impact - must account for these + Definitions: n_o - number of seed electrons n_s - number of secondary electrons, from ion bombardment n_ei - number of electron ion pairs produced n_t - total number of electron leaving negative electrode

5 number of secondaries produced per unit path legth of the primary electron second Townsend coefficient to find current in the gap, take x --> d, the gap length breakdown condition A good empirical relation for alpha is P - pressure (gas density) E - electric field, V/d

denominator varies slowly since it is the logarithm Gas breakdown voltage is approximately equal to a constant times background gas pressure, times gap length + By changing pressure, or gap length,

6 denominator varies slowly since it is the logarithm Gas breakdown voltage is approximately equal to a constant times background gas pressure, times gap length + By changing pressure, or gap length, we can make a switch that will hold off high voltages + Doesn't say much about state of switch after breakdown, just that "current is infinite." Obviously, this isn't true. + The Paschen curve is different for different gases, electrode shapes, etc. So it must be empirically found for any switch. + This rule also works for breakdown in places we don't want it - arc short circuits, surface flashovers in gases, other bulk breakdowns. If you want to increase the hold-off, increase pressure and/or distance. + The Townsend model is best, or most representative, at low gas pressures. At higher pressures, we get streamers.

7 Streamer formation + Townsend works for high E/p (low pressure) + High pressure, get filamentary discharges (somewhat like lightning) Streamer theory (after Meek 1940) + get Townsend style ionization at first, but it builds up and positive charges start to stick around + electric field at head of discharge gets large, approaches the applied field + electrons are drawn to the head prefentially, it grows, becomes a streamer. Townsend like Streamer assume + charges in the head are spherical in shape, the electric field at the head is number of ions formed in avalanche ions in cylinder of radius r, length dx

8 The avalanche radius is determined by diffusion, or a random walk of the particles after collisions. Characterized by a diffusion coefficient, D = (step size)^2/(2 * (time between steps)). Get a streamer when E_1 --> E, x --> d + Formula isn't very useful, but sketches the theory. + since alpha depends on V, P, and d, and E=V/d, we still have an expression with V, P, and d depending on constants of the gas + Most studies of streamers now are numerical + Note electrons ahead of the streamer are attributed to photoionization and runaway electrons leaving the head.

9 Diffusion, Mobility and Conductivity + What happens after the streamer connects, or the Townsend discharge results in a conductive switch? + The switch becomes a resistor (and possible inductor in series combo) If we have an ionized gas undergoing lots of collisions, in an electric field + the electrons cannot accelerate in the field, collisions keep slowing them down + We can describe the force balance on the electrons The electric field pulls on the electrons Allow a pressure gradient to push on the electrons There is a drag due to collisions Defining the momentum transfer collision frequency And the momentum change due to collisions, m - electron mass, n - electron density, v - electron average velocity Current density and flux are

10 Defining the mobility and diffusion coefficient mobility diffusion coefficient + we did this for electrons, but it works for ions too. Just use the correct momentum transfer cross section, velocity, charge and mass. + when we combine ions and electrons, we need a combined diffusion coefficient, ambipolar diffusion coefficient. Not too important in our case. + we can come up with a more familiar form of Ohm's law.

11 Note that in a switch, mobility is a function of temperature, and temperature and density are functions of time. Hence conductivity and resistance are very time dependent in gas switches

12 The Switch Arc + Assume a switch with voltage V + A streamer has connected across the switch + Initially the plasma density is low, so the conductivity is low Braginskii theory + After streamer connection, channel rapidly heats by (I^2)R + Temperature and pressure rise rapidly + Results in a cylindrically expanding shock wave + Energy loss - hydrodynamic (from expansion) radiation + Energy gain - (I^2)R heating + Balance loss and gain to keep temperature and conductivity constant (this is a weak point) + Braginskii solved for the channel radius versus time initial radius [m^2] undisturbed gas density [kg/m^3] related to ratio of specific heats, ~4.5 for gamma=5/4 conductivity (from low density plasma, or high temperature plasma) [(Ohm*m)^-1] discharge current [A]

13 Can use Braginskii to come up with time dependent resistance and inductance radius of the current return, assuming a coaxial, cylindrically symmetric switch

Plasma Physics Prof. Vijayshri School of Sciences, IGNOU. Lecture No. # 38 Diffusion in Plasmas

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