An estimation of critical electron density at just starting breakdown in gases
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An Estimation of Critical Electron Density at Just Starting Breakdown in Gases. Mase. H Professor Emeritus of Ibaraki University. Ionization Potential. m.f.p. for electron impact ionization. cf E * = 30 kV/cm for dielectric strength in atmospheric air

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An Estimation of Critical Electron Density at Just Starting Breakdown in Gases

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An estimation of critical electron density at just starting breakdown in gases

An Estimation of Critical Electron Density at Just Starting Breakdown in Gases

Mase. H

Professor Emeritus of Ibaraki University


Electric field threshold e for electron impact ionization of neutral atoms

Ionization Potential

m.f.p. for electron impact ionization

cf E* = 30 kV/cm for dielectric strength in atmospheric air

If fi = 15 V , li becomes 5x10-4 cm ← reasonable

Electric Field Threshold E *for Electron Impact Ionization of Neutral Atoms


Temporal and spatial growth of electron density

Temporal and Spatial Growth of Electron Density


Structure of electron avalanche

cf ions are at rest

initial electrons;

1.spontaneously generated

2.externally generated

(pre-ionization)

3.photo-ionization due to light

emission from front of

avalanche (feedback)

4.2ry emission by ion bom-

bardment (g process, feedback)

Length x’of electron avalanche

ne’

electron cloud

ne*

ne0

ne0

ion space charge

ion space charge

plasma

x’

E*

x*

Structure of Electron Avalanche

before and after starting breakdown


Scenario of starting electric breakdown in gases

E > E*

anode

cathode

front-sheath

moving

micro-plasma column

1. E > E* is applied field across the electrodes. ne0 occurs at any time.

2. dne/dt > 0 in front of electron avalanche. E is extremely distorted by the space charge.

3. ne = n* = nin* is the critical electron density at just starting breakdown.

>> appearance of micro-plasma in front of electron avalanche or near the anode.

4. E is increasing in the space between the cathode and front of the plasma column >> enhanced ionization >> expansion of plasma column.

5. Front of the plasma column (that is virtual anode) is moving toward the cathode. go back # 4. < positive feedback process > (* More detailed discussion is required to introduce the energy minimum principle.)

6. When the front-sheath comes at the cathode, the discharge gap makes it to flashover .

7. If the front–sheath satisfies the self-sustaining condition of discharge , the glow discharge or the arc discharge occurs.

In the case, the front-sheath means so-coaled “cathode sheath”. ( Appendix II )

Scenario of Starting Electric Breakdown in Gases


Evolution of potential structure before and after starting breakdown

V(t)

Front of plasma column

V(x,t)

x

I(t)

Cathode sheath

Evolution of Potential Structure before and after Starting Breakdown

Starting breakdown

Stable discharge


A hypothesis for the appearance of micro plasma at anode near region

E* would be shielded electrically by the polarization of plasma particles. It is best that Tev should be confirmed theoretically by the plasma balance equation. Usually TeV is in the range of several eV.

A Hypothesis for the Appearance of Micro-Plasma at Anode Near Region

TeV electron temperature in eV

lD Debye shielding length


Critical electron density n e at just starting breakdown in gases

Critical Electron Density ne*at Just Starting Breakdown in Gases


Relationship between critical electron density and space charge density in front sheath

Relationship between critical electron density and space charge density in front-sheath


N e n i and l d l i as a function of t ev e f i

ne*/ni

ne*/ni

lD/li

lD/li

0.01

0.1

TeV/efi

ne*/ni and lD/li as a function of TeV/efi


Relationship between micro plasma column and its front sheath at starting breakdown

anode

cathode

E > E*

front-sheath

micro-plasma column

moving

space charge density in front-sheath

potential structureat starting breakdown

TeV

fi

nis

ne*= (efi/TeV )nis

f

ne~0

li

lD = (TeV/efi )li

Relationship between Micro-Plasma Column and its Front-Sheathat Starting Breakdown


Velocity v fs of moving front sheath streamer

ionization & electron heating

front-sheath

plasma expansion

li, fi

lD

+

e

e

e

Velocity vfs of Moving Front-Sheath (Streamer).

The growth of plasma volume is caused by the ionization due to fast electrons having their energy of (1/2)mv2 > efi.

cf : expansion due to electron heating is neglected here

recent observation of vfs ~108 cm/s


Velocity v fs of moving front sheath streamer1

ionization & electron heating

front-sheath

plasma expansion

+

li, fi

e

e

e

Velocity vfs of Moving Front-Sheath (Streamer).

Expansion of micro-plasma is caused by the ionization due to fast electrons having their energy of (1/2)mv2 > efi. Velocity of moving front-sheath may be determined by the motion of fast electrons which are passing through the front-sheath without any ionization collision. So, vfs could beestimated to be the same velocity of electrons accelerated up to efi eV

(* More detailed discussion is required to introduce the energy minimum principle.)

cf : recent observation of vfs ~108 cm/s


Critical current density at starting breakdown 1 2

Critical current density at starting breakdown 1/2

Velocity and density of fast electrons which are passing through the front-sheath


Critical current density at starting breakdown 2 2

Critical current density at starting breakdown 2/2

electron thermal velocity

Cross-section of micro-discharge in atmospheric pressure

1 mm2→ I *~ 60 mA

0.01 mm2→ I *~ 0.6 mA


Summary

E* is shielded electrically by the polarization of plasma particles

Summary

Following hypothesis for the appearance of micro-plasma at anode near region, seems to be correct. Breakdown is just starting when the micro-plasma appears at anode near region.

We can estimate the critical electron density at just starting breakdown by using the above formula.


Summary continue

Summary continue

We also discus the propagation of plasma column head toward the cathode (streamer). The propagating speed of plasma column head might be determined by the motion of fast electrons which are passing through the front-sheath without any ionization loss and then vfs could beestimated to be the same velocity of electrons accelerated up to efi eV (* More detailed discussion is required to introduce the energy minimum principle.)


Appendix i

Appendix I

Recent Observation of Streamer

-Kumamoto Univ.-

Vs=7.1 mm/nS

Fig. 7 Streak photograph


Appendix ii

anode

plasma

cathode

L

je

ji

Vcs

dcs

cathode sheath

Cathode Sheath in Steady State Glows

Appendix II

* Here we consider only the most essential processes


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