Dynamics of the breakdown of the discharge gap at high overvoltage

A. Shvydky (University of Toledo, OH),

V.N. Khudik (Plasma Dynamics Corp., OH),

V.P. Nagorny (Plasma Dynamics Corp., OH),

C.E. Theodosiou (University of Toledo, OH)

ABSTRACTThe dynamics of the breakdown of the discharge in a gap between two plane electrodes at high over-voltage is studied via 3D Monte Carlo/PIC kinetic simulations. In these simulations, the negative and positive macroparticles represent exactly their physical counterparts (which cannot in principle be attained in 1- or 2-D Monte-Carlo simulations, since macroparticles there are planes or rods rather than point particles). The breakdown is initiated by a single seed electron, and then an ionization region formed at the anode spreads toward the cathode. The velocity of this spreading (as well as the ionization region structure) at different voltages applied to the gap is compared with those predicted by the 1D analytical theory. Such realistic simulations allow the elucidation of the role of fluctuations in microdischarges, when the gap width is small and the number of particles is relatively low.

Geometry, parameters, and assumptions• Pure Neon gas

• Pressure p=500 Torr

• Gap Length d=100–800 m

i.e. pd = 5–40Torr cm

• Initial voltage across the gap is much larger than the breakdown voltage

• Secondary electron emission coefficient due to ions ion = 0.64

• No photoemission from the cathode

*Cross-sections were taken from SIGLO DataBase

`http://www.siglo-kinema.com/database/xsect/siglo.sec'.

)11

ln(ion

danode

cathode

V

0E d

Features of MC/PIC code

• One ion/electron is represented by just ONE macroparticle!

• Total of up to 250 million of ions and electrons are tracked on a up to 64 processors (on Linux clusters at the Ohio Supercomputer Center)

• Up to 150x150x150 meshes are used

• FFT method is used for solution of Poisson equation

Gap Length 200m, Voltage 400V

200 100 0 100 2000

100

200

Potential time272.83 ns

200 100 0 100 2000

100

200Ion Density time272.83 ns

200 100 0 100 2000

100

200Ion Density time310.44 ns

200 100 0 100 2000

100

200

Potential time310.44 ns

Gap Length 200m, Voltage 400V

200 100 0 100 2000

100

200

Potential time317.19 ns

200 100 0 100 2000

100

200

Potential time323.04 ns

200 100 0 100 2000

100

200Ion Density time323.04 ns

200 100 0 100 2000

100

200Ion Density time317.19 ns

Longitudinal uniformization of plasma trail

Longitudinal electric field along the midline of the discharge at time moments

t1=272.83ns, t2=310.44ns, t3=317.19ns, t4=323.04ns

50 100 150 200x,m

20

20

40

60

80

100

120

E,V

cm Torr Longitudinal electric field

1t

2t

3t

4t

When ionizing wave approaches the cathode and the cathode fall starts to form, the electric field in the plasma trail becomes uniform

Transverse uniformization of plasma trail

25 50 75 100 125 150 175 200x,m

50

100

150

200

250

300

E,V

cm Torr Longitudinal electric field

Electric field in the plasma trail becomes uniform also in the transverse direction

Longitudinal electric field along the midline (red), 40um (blue) off the midline , and 80um (green) off the midline

Gap Length 400m, Voltage 600V

400 200 0 200 4000

200

400Ion Density time 328.25 ns

400 200 0 200 4000

200

400Potential time 328.25 ns

400 200 0 200 4000

200

400Ion Density time 384.2 ns

400 200 0 200 4000

200

400Potential time 384.2 ns

Gap Length 400m, Voltage 600V

400 200 0 200 4000

200

400Potential time 394.92 ns

400 200 0 200 4000

200

400Ion Density time 394.92 ns

400 200 0 200 4000

200

400Ion Density time 400.07 ns

400 200 0 200 4000

200

400Potential time 400.07 ns

Size of Ionizing Wave•Longitudinal size of the ionizing wave is determined by the ionization coefficient

• Transversal size is controlled by the electron diffusion, since in the case of zero electron diffusion coefficient the transversal wave size reduces to zero (as seen from the presented figures)

200 670

400

Ion Density time453.43 ns

200 680

405

Potential time453.43 ns

Case Te=0

Gap Length 600m, Voltage 800V

600 300 0 300 6000

300

600Ion Density time 501.05 ns

600 300 0 300 6000

300

600Potential time 501.05 ns

600 300 0 300 6000

300

600Ion Density time 550.78 ns

600 300 0 300 6000

300

600Potential time 550.78 ns

Gap Length 600m, Voltage 800V

600 300 0 300 6000

300

600Ion Density time 566.51 ns

600 300 0 300 6000

300

600Potential time 566.51 ns

600 300 0 300 6000

300

600Ion Density time 573.39 ns

600 300 0 300 6000

300

600Potential time 573.39 ns

Speed of Ionizing Wave

100 200 300 400 500 600x,m

106

2106

Vf,cms Ionizing Wave Velocity

100 200 300 400 500 600x,m

2

4

6

8

10

VfionEcath Relative Velocity

Wave velocity increases as it moves toward the cathode

Relative wave velocity normalized to the ion velocity at the cathode goes through a maximum

400 0 4000

400

800Ion Density time 124.51 ns

400 0 4000

400

800Ion Density time 129.77 ns

400 0 4000

400

800

Potential time 121.76 ns

400 0 4000

400

800Ion Density time 121.76 ns

400 0 4000

400

800

Potential time 124.51 ns

400 0 4000

400

800

Potential time 129.77 ns

Gap Length 800mm, Voltage 1200V

Gap Length 800mm, Voltage 1200V

400 0 4000

400

800Ion Density time 134.23 ns

400 0 4000

400

800Ion Density time 138.13 ns

400 0 4000

400

800Ion Density time 141.32 ns

400 0 4000

400

800

Potential time 134.23 ns

400 0 4000

400

800

Potential time 138.13 ns

400 0 4000

400

800

Potential time 141.32 ns

120 125 130 135 140 145time,ns

0.5

1

1.5

2

2.5

3

Number of Ions hitting the cathode during the time step

120 125 130 135 140time,ns

0.0002

0.0004

0.0006

0.0008

0.001

I,Acm Discharge Current

• Erratic movement of the ionizing wave corresponds to individual ions hitting the cathode

Erratic ionizing wave movement at high avalanche multiplication

CONCLUSION• Uniformization of the plasma trail is similar to 1D case • Longitudinal size of the ionizing wave is controlled by the

ionization coefficient and is proportional to ,while the transverse size is controlled by the electron diffusion

• While the ionizing wave moves toward the cathode, its velocity increases. The relative velocity (to the ion velocity at the cathode) may experience maximum if the initial electric field in the gap corresponds to the right branch of the Paschen curve

• When the charge charge produced by an avalanche originated by just a single electron emitted from the cathode is comparable with the charge at the tip of the ionizing wave, its front moves erratically