COMSOL 6.4 - DC Breakdown Voltage of Parallel Electrodes in Air

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DC Breakdown Voltage of Parallel Electrodes in Air

This simulation model focuses on electrical breakdown in air at atmospheric pressure, where streamer breakdown is the dominant mechanism. Unlike glow discharges, streamer discharges are unstable and marked by a rapid rise in discharge current due to electron impact ionization (see Fig. 7.1 in Ref. 1).

The model computes the DC breakdown voltage between parallel electrodes in air using a charge transport formulation. While implemented in one dimension for simplicity, the approach can be generalized to other gases and extended to higher dimensions. Validation against published experimental data shows that the model reproduces breakdown behavior with high accuracy.

Model Definition

The Electric Discharge interface is used to compute the discharge current. The built-in charge transport model is used:

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e, p, n denote electrons, positive ions, and negative ions

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ni is the number density of the charge carrier (SI unit: 1/m3)

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E is the electric field (SI unit: V/m)

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zi denotes the carrier charge (SI unit: 1)

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μi denotes the carrier mobility (SI unit: m2/(V·s))

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wi is the drift velocity in the electric field (SI unit: m/s)

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Di is the diffusion coefficient (SI unit: m2/s)

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Ri is the reaction rate (SI unit: 1/(m3·s))

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α is the ionization coefficient (SI unit: 1/m)

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η is the attachment coefficient (SI unit: 1/m)

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βep is the electron–ion recombination coefficient (SI unit: m3/s)

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βpn is the ion–ion recombination coefficient (SI unit: m3/s)

The above transport equations are fully coupled with Poisson’s equation through the electric field and the space charge:

where e is the elementary charge.

The breakdown is identified by a sharp increase in current caused by an electron avalanche. To capture this behavior, the model performs a parametric sweep of the applied voltage. The simulation automatically terminates once the discharge current exceeds a defined threshold.

Results and Discussion

Figure 1 shows the current–voltage (I–V) characteristics. As can be seen, there is a region where the discharge current increases sharply for each air gap distance. Figure 2 compares the breakdown voltages and corresponding electric fields as a function of gap distance for three different material datasets. The simulated results exhibit good agreement with experimental measurements (see Fig. 7.4 in Ref. 1).

Figure 1: The current-voltage characteristics of the discharge for different air gaps.

Figure 2: The simulated breakdown voltages as a function gap distance for three different material datasets.

1. Y.P. Raizer, Gas Discharges Physics, Springer, 1997.

Electric_Discharge_Module/Electrical_Breakdown/breakdown_voltage_dc

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > .

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In the tree, select > .

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
V0	10[kV]	10000 V	Applied voltage
d	1[cm]	0.01 m	Gap length

Interval 1 (i1)

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In the window, expand the > node.

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Coordinates (cm)
0
d

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Material Switch 1 (sw1)

In the window, under right-click and choose > .

Add Material from Library

In the toolbar, click

and choose .

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Go to the window.

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In the tree, select > > > .

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Right-click and choose .

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In the tree, select > > > .

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Right-click and choose .

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In the tree, select > > > .

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Right-click and choose .

Electric Discharge (edis)

In the window, under > click .

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

In the window, click .

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In the toolbar, click

and choose .

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Select Boundary 2 only.

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In the window for , locate the section.

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In the V0 text field, type V0.

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Locate the section. From the list, choose .

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the window, right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 200.

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In the text field, type 5.

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Select the checkbox.

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Parametric Sweep

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
d (Gap length)	0.05 0.1 0.2 0.4 0.6 0.8 1	cm

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In the toolbar, click

and choose .

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In the window for , locate the section.

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Step 1: Electrostatics Initialization

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In the window, click .

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In the window for , click to expand the section.

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Select the checkbox.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
V0 (Applied voltage)	1000	V

Step 2: Stationary

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In the window, click .

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In the window for , click to expand the section.

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Select the checkbox.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
V0 (Applied voltage)	10^{range(log10(1000),1/100,log10(50000))}	V

Solution 1 (sol1)

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In the toolbar, click

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In the window, expand the node.

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In the window, expand the > > > node.

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Right-click > > > > and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Stop expression	Stop if	Active	Description
comp1.edis.I0_1>1e-5[A]	True (>=1)	√	Stop expression 1

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Locate the section. From the list, choose .

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In the window, under > > > click .

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In the window for , click to expand the section.

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In the text field, type 250.

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In the window, click .

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In the window for , locate the section.

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Clear the checkbox.

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In the toolbar, click

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Breakdown Voltages & Fields

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In the toolbar, click

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In the window for , type Breakdown Voltages & Fields in the text field.

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Locate the section. From the list, choose .

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Locate the section. Select the checkbox.

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Select the checkbox. In the associated text field, type Breakdown Voltage, kV.

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Select the checkbox. In the associated text field, type Breakdown Field, kV/cm.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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In the list box, select .

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From the list, choose .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
V0	kV	Air [Kang et al. 2003]

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Locate the section. From the list, choose .

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In the text field, type d.

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Click to expand the section. Find the subsection. From the list, choose .

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Right-click and choose .

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In the window for , locate the section.

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In the list box, select .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
V0	kV	Air [Morrow and Lowke, 1997]

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Right-click and choose .

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In the window for , locate the section.

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In the list box, select .

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Locate the section. In the table, enter the following settings:


Expression	Unit	Description
V0	kV	Air [Kulikovsky, 1998]

Global 1, Global 2, Global 3

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In the window, under > , Ctrl-click to select , , and .

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
V0/d	kV/cm	Air [Kang et al. 2003]

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Locate the section. Select the checkbox.

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Locate the section. Find the subsection. From the list, choose .

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From the list, choose .

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Find the subsection. From the list, choose .

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In the window, click .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
V0/d	kV/cm	Air [Morrow and Lowke, 1997]

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Locate the section. Select the checkbox.

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Locate the section. Find the subsection. From the list, choose .

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In the window, click .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
V0/d	kV/cm	Air [Kulikovsky, 1998]

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Locate the section. Select the checkbox.

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Locate the section. Find the subsection. From the list, choose .

Breakdown Voltages & Fields

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In the window, click .

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In the window for , click to expand the section.

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From the list, choose .

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Locate the section. From the list, choose .

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button in the toolbar.

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button in the toolbar.

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In the toolbar, click

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In the window for , type IV Curve in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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Locate the section. From the list, choose .

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Locate the section. Select the checkbox.

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Locate the section. From the list, choose .

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In the text field, type 3.

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Right-click and choose .

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In the window for , locate the section.

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In the table, enter the following settings:


Expression	Unit	Description
edis.I0_1	A	Terminal current

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Locate the section. From the list, choose .

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Locate the section. Find the subsection. From the list, choose .

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From the list, choose .

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Click to expand the section. Find the subsection. Clear the checkbox.

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Clear the checkbox.

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Find the subsection. In the text field, type d = eval(d,cm) cm.

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In the toolbar, click

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button in the toolbar.