Discharge Cell Design. Some initial explorations, considerations and open questions

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Brook Garrison
5 years ago
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1 Discharge Cell Design Some initial explorations, considerations and open questions

2 Modelling plasma discharge circuit demands Based on paper from SPARC-LAB experiment (Nuc. Instrum Meth A 2015) Design of a plasma discharge circuit for particle wakefield acceleration, M.P Anania et. al. Code written in Mathematica Plasma has Spitzer Resistivity and a high resistance component for low ionisation Aim to get order of magnitude circuit requirements Looks at electron temperature versus time for variety of gas pressures and circuit demands No temperature loss processes modelled.

3 Building up a model Write temperature growth as: Thermal capacity at constant volume Capillary dimensions Temperature - Note no loss terms just Joule heating Discharge trigger current Plasma resistivity

4 Building up a model Looking at plasma resistivity: Resistivity due to ion - electron collisions. Can use well established Spitzer formula for this: Coulomb Log - here set to 10. Not going to go down that rabbit hole Ionization degree Introduced a temperature dependance

5 The ionisation degree This model uses the Saha equation: This equation is only valid for weakly ionised plasmas and in thermal equilibrium. It is probably one of the weaker areas of the model. We define our ion (i), atom (a) and electron (e) densities (n) as: The density of neutrals (n) in the plasma state is then given by Note the atom density is given by ideal gas law at T = 300K This provides a basis for rewriting the Saha equation

6 The ionisation degree The Saha equation is normally written as Ionisation energy of 1st electron. All cases for hydrogen: 13.6 ev Using the previous definitions we can write And we have Z in terms of pre-defined parameters

7 The ionisation degree Not an easy equation to deal with, but with some computational tweaks can get a form for Mathematica to use Need to make sure Z is defined: 0 < Z < 1

8 Spitzer resistivity Now have all the information to plot the Spitzer resistivity: Problem! Suggests neutral gas has no resistance...

9 Resistivity from atom-electron collisions Started with: Following a similar procedure to Spitzer formula: Using a Maxwell distribution for the velocity of electrons in this process Redefining some terms to give an ionisation degree Gas pressure Good behaviour for Z ~ 1

10 Resistivity from atom-electron collisions Problem solved?

11 Modelling the current This is where the circuit parameters are included We model a simple discharge RLC circuit Where the inductance is parasitic and comes from the capacitor. Set to 600nH for all cases For example: We add a plasma cell here, which is essentially a temperature (time) dependant resistor

12 Modelling the current We can now write an ODE for the dependence of current on time Which looks like a nice equation, but Care that reasonable solutions are given. Code validated against examples given in the reference paper at every step.

13 Parameters given for SPARC-LAB Taken from their paper: Peak Voltage: 20 kv Peak Current: 500 A Capacitance: 6 nf High Voltage - Low capacitance regime Gas pressure: 1.5 mbar Capillary length: 3 cm Density: 3.6 x10 22 m -3

14 Temperature Rise

15 Parameters from Russian paper for IMP source Taken from their paper: Peak Voltage: 5kV Peak Current: 50 A Capacitance: 3 μf -> Low(er)Voltage - High capacitance regime (bank of capacitors) Gas pressure: 5 mbar Capillary length: 16 cm Density: 1.3 x10 23 m -3

16 Temperature Rise

17 Parameters from a Cockcroft source Taken from discussions: Peak Voltage: 5kV Peak Current: 50 A Capacitance: 30 nf -> Low Voltage (for our source) - Moderate capacitor regime (need to achieve this) Gas pressure: 0.15 mbar Capillary Length: 10 cm Density: 5 x x10 21 m -3 - Middle of range explored in recent paper

18 Temperature Rise

19 AutoCAD drawings Explorations of how to hold electrodes and support gas capillary. Gives an idea of what extra components are needed and other design considerations. From the start looking to create a modular design - so length can be extended easily. Note that a test/diagnostic platform may look different & have different materials compared to a vacuum one.

20 A first atempt Open questions: Material? Machining? Electrical insulation, heat, outgassing

21 Two gas tubes, 2 Electrodes

22 Double cathode, single anode design

23 Holding the electrode Side View Glass or ceramic? Electrical insulation, heat, outgassing

24 Use of beads for extra insulation

25 Gas & Plasma distributions For a discharge plasma in a non-flowing background gas we expect to see higher electron densities close to the cathode. For a gas flowing into a capillary at a T-junction we anticipate higher gas density at the junction. These effects need to be modelled for the capillary dimensions and voltages we will use. It will likely impact plasma uniformity and gas flow rates - which will affect our vacuum isolation design Need a CFD code & a plasma code

26 Possible mitigating design Cathode Anode Gas flow close to anode Cathode High e- density High gas density Can a balance then be achieved? High e- density Another idea would be to have a central cathode and gas flow close to capillary ends.

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