Lecture 5: High Voltage and Pulsed Power

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Lucas Lewis
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1 Lecture 5: High Voltage and Pulsed Power Reviewing our processes in Applied EM and EP + We create charged particles, by application of thermal, electrostatic, or electrical discharge energy + We store energy in the charged particles by accelerating them in strong electric and magnetic fields + We use that stored energy somehow, to make HPM or x-rays, or to inject the charged particles into another accelerator for further energy storage by electromagnetic means Clearly we need to put energy into the created charged particles. We usually do this electrostatically, perhaps with help from magnetostatic fields that guide or focus our charge. We know a charged particle feels a force due to an electric field. We can calculate kinetic energy (non-relativistically)

2 So, if we apply a voltage, phi, we can increase our particle kinetic energy as it moves through that potential. We can apply that voltage as DC or as a pulse. DC voltage sources: HV transformer and diodes Filtering capacitor High voltage transformer Diode string to rated voltage DC voltage sources: Cockroft-Walton generator DC voltage sources: Van de Graaf generator Charge injection Belt High voltage point Insulator Mechanically moves charge to create DC high voltage

3 Sometimes DC won't work for us, and we need a pulsed voltage + Fast pulses can apply voltage before detrimental effects like breakdown can occur + Pulsed voltages can enable time resolution. E.g. a fast x-ray pulse can be generated to look at fast phenomena + Some applications require high powers. With pulses, high peak powers at very low duty cycles can be achieved, resulting in low overall energy + Some acceleration mechanisms, like induction accelerators and betatrons are inherently pulsed. Pulsed power systems are a variant on the LCR circuit Here, the capacitance is initially charged to V_o by some external (possibly DC, possibly pulsed) source, and the switch is initially open. The switch then closes and the capacitor discharges through the load. The governing equation is defining

4 We have 3 classes of solution, underdamped, overdamped and critically damped Underdamped Overdamped Critically damped We have maximum energy transfer from the capacitor to the load resistor for the critically damped circuit. The characteristic impedance of this generator is

generator: extending to high voltage + The Marx generator provides a way to get to higher voltage, by using multiple stages of capacitance + The output pulse looks very similar to the RLC circuit (to

5 We could build a pulse generator this way. + Charge one capacitor to V (limits to about 100 kv) + Adding inductance to set pulse length, or use the inherent self-inductance of cabling + Using the internal resistance of the components Marx generator: extending to high voltage + The Marx generator provides a way to get to higher voltage, by using multiple stages of capacitance + The output pulse looks very similar to the RLC circuit (to zeroth order) + Multi-staging is achieved by charge the capacitance in parallel and discharging in series, via several switches Charging resistors Capacitors Switches Operation: + The capacitors are charged to V, through the charging resistors while the switches (could be gas or solid state) are open + The switches close, either by triggering or by self-breakdown, when V is high enough to break down the switch. Interestingly, only the switches nearest the charging input must be triggered, since all the higher switches are over volted by this. + With switches closed, the charging resistors look like open circuits, and the capacitors are now connected in series, producing high voltage. + Since we can lump the capacitance, switch resistance, and internal inductance into single circuit elements, if we include an output switch and load impedance, the circuit looks like an RLC circuit External switch

6 Pulse Forming Line: single stage pulse generator We can use transmission lines to form pulses. + We charge the transmission line with DC or with a pulsed high voltage, say from a Marx generator or a capacitor charging circuit + At the output of the transmission line, we again have a switch connecting the line to a load + When we close the switch, voltage appears across the load until the transmission line is discharged. Transmission line basics Forms two line strip line co-axial Characterized by two conducting surfaces separated by insulator Characteristic impedance: for a loss less or low loss line, given by the constitutive parameters of the insulator (e.g. vacuum, air, polyethylene, etc.) A pulse or wave on the line moves at the phase speed.

7 For a line terminated in an impedance, or for the junction of two transmission lines, some of the pulsed will be reflected, and some will be transmitted. The reflection coefficient is Pulsed power example, a transmission line with an output switch and a matched load (i.e. gamma = 0), charging generator has infinite impedance (gamma = 1). t~0, switch is just closed, line charged to V_g, but load feels V_g/2. Negative pulse starts to move toward the generator at v_p.

8 t~l/v_p, negative pulse reflects off of generator (gamma = 1) and returns to load t~2l/v_p, pulse finishes. The load has felt a pulse of length 2L/ v_p, at voltage V_g/2. Limitations: + To get longer pulses, may need a *really* long line + Likely limited in peak voltage (though can build water lines and magnetically insulated lines to MV levels) + Output voltage is input voltage divided by 2.

9 Pulse-forming network We can model a transmission line as a series of LC circuit loops The PFN is very similar to the PFL, however we have more freedom of design. We can tailor the pulse length more easily by choosing appropriate values of L and C. Blumlein pulse generators: staged pulsed forming lines Take the following pulse forming line circuit

10 Redrawing the circuit this way is helpful when swx closes t=0, swx closes, short circuit pulse travels down first line toward load t>l/v_p, pulse has reflected off load, gamma=1/2, or half relfects, and half enters line 2 t>2l/v_p, pulse reflect off closed swx in line 1, gamma=-1, pulse reverses polarity. Also pulse reflects off of open end of line 2, gamma=1, returns to load Total voltage across load V=V_o/2+V_o/2=V_o

11 So, pulse lasts as long as a single transmission line, but full charge voltage across the load. Can also do multiple stages of Blumlein pulse generators

A Low Impedance Marx Generator as a Test bed for Vacuum Diodes

A Low Impedance Marx Generator as a Test bed for Vacuum Diodes Biswajit Adhikary, P Deb, R.Verma, R. Shukla, S.K.Sharma P.Banerjee, R Das, T Prabaharan, BK Das and Anurag Shyam Energetics and Electromagnetics