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Influence of magnetic fields on negative corona discharge currents

Junfeng Mi, Dexuan Xu*, Yinghao Sun, Shengnan Du, Yu Chen

Laboratory of Discharge Plasma and Pollution Control Engineering, Department of Environmental Science and Engineering,

Northeast Normal University, Changchun 130024, China

a r t i c l e i n f o

Article history:

Received 1 July 2007

Received in revised form 31 March 2008

Accepted 16 April 2008

Available online 28 May 2008

Keywords:

Magnetically enhanced

Negative corona discharge

Plasma

a b s t r a c t

The mechanism of magnetically enhanced negative corona discharges was studied by comparing the

influences of two different magnetic fields on the negative corona discharge current. In the magneticallyenhanced corona discharge, a local magnetic field is formed near the discharge electrode by using the

small permanent magnets, and the corona discharge currents are enhanced because the Larmor

movements of free electrons enhance the ionizations of the gas molecules in the ionization region. It is

assumed that the increase of the discharge currents attributes to only the enhanced ionization process in

the small ionization region, and is not relevant to the lengthening trajectory of free electrons in the wide

drift inter-electrode region. In the enhanced ionization-region magnetic field, the mechanism of mag-

netically enhanced corona discharges was explained and the relative increase of the discharge current

could exceed 150%. However, in a weakened ionization-region magnetic field, the mechanism of mag-

netically enhanced corona discharges was inconspicuous and the relative increase of the discharge

current could only reach about 25%. It is predicted that after the magnetic field of magnetically enhanced

negative corona discharges had been fixed, the relative increases of the discharge current for varied

mean electric fields in the inter-electrode region could have a maximum value, according to the

mechanism of magnetically enhanced negative corona discharges. The above predication was completely

validated by the current experiment data. In addition, the optimum combinations between the electric

field and the magnetic field were obtained. In order to reach the largest relative increase of the discharge

current under 4 kV/cm mean electric field intensity in the inter-electrode region for a practical elec-trostatic precipitator, the optimum magnetic field with a magnetic flux density of about 0.43 T at the

edges of magnetic st rings should be selected.

2008 Elsevier B.V. All rights reserved.

1. Introduction

Recently, more and more countries are beginning to limit the

emissions of micron and sub-micron aerosol particles. Thus the

corona discharges have progressively employed for electrostatic

precipitators (ESP) and pre-chargers as well as some new applica-

tions, such as sterilization [1], the enhancement of chemical vapor

deposition [2], separation [3], and the production of ozone [4].The theory for charging particles is well developed for the better

application of ESP. Pauthenier and Moreau-Hanot [5] developed an

expression for field charging of large aerosol particles. Fuchs and

Bricard developed the same statement for diffusion charging of

smaller aerosol particles, and the combined field and diffusion

charging theory was discussed by Liu and Kapadia [6]. A few

experimental and theoretical studies [710] indicated that Fuchs

theory had successfully predicted the charging probability of fine

particles. The experimental and mathematical study carried out by

Reischl et al. [11] demonstratedthat Fuchs theory was also valid for

bipolar diffusion charging of fine particles, while the charging

probability of positive ions was less than that of negative ions. In

addition, there was no difference between varied gases and particle

materials. The charges on fine aerosol particles also vary in agree-

ment with diffusion charging theory, which tended to promote the

charging of fine aerosol particles.Based on the above charging theories, the diffusion charging

should be intensified for removal of fine aerosol particles in ESP. In

addition, the diffusion charging will be a determined factor when

the fine aerosol particles pass through ESP with a weak intensity of

the applied electric field as well as a higher gas temperature.

However, the field charging will be a determined factor when the

large aerosol particles pass through ESP with a strong intensity of

the applied electric field and a lower gas temperature [12].

According to the diffusion charging theory of ions, it is advan-

tageous for diffusion charging to supply a higher concentration of

ions when the intensity of the electric field is weaker. However, the

weak electric field could not induce a high concentration of ions in* Corresponding author.

E-mail address: [email protected] (D. Xu).

Contents lists available at ScienceDirect

Journal of Electrostatics

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e l s t a t

0304-3886/$ see front matter 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.elstat.2008.04.010

Journal of Electrostatics 66 (2008) 457462
mailto:[email protected]://www.sciencedirect.com/science/journal/03043886http://www.elsevier.com/locate/elstathttp://www.elsevier.com/locate/elstathttp://www.sciencedirect.com/science/journal/03043886mailto:[email protected]


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the general corona discharges. Therefore, the fine aerosol particles

could be effectively captured when a higher concentration of ions

and weaker electric field are supplied by ESP. In order to charge fine

aerosol particles, it is necessary to enhance the corona discharge

currents in ESP with a weak intensity of electric field.

Researches on enhancing corona discharge current using

a magnetic field have been carried out in recent years. Initially, the

study on a small cylinder corona nozzle posited in the inner-hole of

a cylindrical permanent magnet where a weakened ionization-

region magnetic field was formed, was reported [13]. Although the

propagation of an ionization region was noticed in the experiment,

the influence of the magnetic field on ionization was not given

enough attention. We then conducted research on a magnetically

enhanced corona pre-charger [14]. An enhanced ionization-region

magnetic field was formed by installing a small permanent magnet

near the discharge electrode, which causes the magnetic flux

densityto be higher in the ionization region than in the drift region.

When the magnetic flux density was 0.43 T at the edges of mag-

netic strings, the discharge current was increased by 1.3 times

under a high voltage of 15 kV. The concentration of negative ions in

the charging region of the pre-charger was greatly increased as

well. This result is of great benefit to the charging of fine aerosol

particles. It was supposed that the dominant mechanism of mag-netic enhancement in the corona discharges involves the Larmor

movements of free electrons which enhance ionizations of the gas

molecules near the discharge electrode, and the lengthening

trajectory of free electrons also induces a little increase of corona

discharge current.

In the current study, we conductedthe research on the influence

of the magnetic field on negative corona discharge current to fur-

ther explore the mechanism of magnetically enhanced corona

discharge. Only the magnetically enhanced negative corona dis-

charges were discussed in this paper for its wide use.

2. Experimental apparatus

The magnetic field was applied near the discharge electrode;

herein called the ionization-region magnetic field. The experi-

mental apparatus is shown in Fig. 1. The effective length of the

stainless-steel wire electrode (4) was 10 mm and 0.5 mm in di-

ameter. Two cylindrical, permanent magnet strings (5) of 6 mm in

diameter were made from permanent magnet disks and assembled

at opposite ends of the wire electrode. The magnetic flux density

near the discharge electrode could be changed by increasing or

decreasing the numberof magnet disks in the magnetic strings. The

spacing between the two magnetic strings was kept at 12 mm. The

wire electrode was positioned exactly in the center of stainless

cylinder electrodes (3). The length of cylinder electrode was 70 mm

and its diameter 70 mm. A high-voltage power supply (1) (Beijing

Electrostatic Instrument Factory, China, GJ F 100), capable of de-

livering negative voltage, was measured using a high voltage

divider (2) (Shanghai Huisha Instrument Co., Ltd., China, FRC-50).

Between the cylinder electrode and grounding wire, two ammeters

with different measurement ranges were connected. One ammeter

(Cany Precision Instruments Co., Ltd., China, BS15/6) was used to

measure the corona onset voltage, and the other (Cany Precision

Instruments Co., Ltd., China, BS15/16) was used to measure the

discharge current.

Fig. 2 shows the magnetic and the electric lines of force between

discharge and cylinder electrode when the strongest magnetic flux

density (near magnetic string edge) is 0.43 T. The magnetic lines of

force were approximately perpendicular to the electric lines of

force near the wire electrode. The magnetic flux density of mag-

netic string edges was measured using a gaussmeter (Shanghai NO.

4 Multimeter Manufacturing Co., Ltd., China, CT5 A). It is obvious

that the magnetic flux density gradually decreases from the wireelectrode to the cylinder electrode when a permanent magnet is

applied near the wire electrode, i.e., the influence of the magnetic

field on the ionization region is stronger than the drift region.

In the second experiment, the magnetic field was applied near

the collecting electrode; herein called the drift region magnetic

field. The experimental apparatus is shown in Fig. 3. The effective

length of the stainless-steel wire electrode (4) was 70 mm and

0.5 mm in diameter. The length of the cylinder electrode (3) was

100 mm, with an insidediameterof 56 mmand an outside diameter

of 60 mm. The cylinder magnet (5) was made from permanent

magnet rings and was installed outside the cylinder electrode, and

the cylinder magnet was 50 mm long with an inside diameter of

60 mm and an outside diameter of 72 mm. The magnetic flux

density in theentire inter-electrode regioncouldalso be changed byincreasing or decreasing the numberof magnet rings of the cylinder

magnet. The wire electrode was positioned exactly in the center of

the cylinder electrode (3). The functions of the high-voltage power

Fig.1. Schematic of experimental apparatus with the ionization-region magnetic field.

1. HV power supply, 2. HV divider, 3. cylinder electrode, 4. wire electrode, and 5.magnet strings.

Fig. 2. Schematic of the magnetic lines of force and the electric lines of force in theionization-region magnetic field.

J. Mi et al. / Journal of Electrostatics 66 (2008) 457462458


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supply (1) and the high voltage divider (2) in this experiment wereaccordant with those in the experiment of the ionization-region

magnetic field.

Fig. 4 shows the magnetic and the electric lines of force between

the wire and cylinder electrodes when the mean magnetic flux

density is 0.015 T near the wire electrode in the drift region mag-

netic field experiment. The strongest magnetic flux density is

0.39 T. In order to determine the mean magnetic flux density near

the wire electrode, four equidistant points on the axis in the ioni-

zation region were considered. The average of the four values was

taken as the mean magnetic flux density in the ionization region.

It is obvious that this permanent magnet could induce a stron-

ger magnetic field in the drift region than that in the ionization-

region magnetic field. The magnetic lines of force were also

approximately perpendicular to the electric lines of force near thewire electrode. Clearly, the magnetic flux density gradually in-

creased from the wire electrode to the cylinder electrode.

3. Influence of magnetic fields on the currents of negative

corona discharges

As seen in Fig. 5, the corona discharge current was greatly en-

hanced by increasing the magnetic flux density in the ionization-

regionmagnetic field. When the magnetic fluxdensity was0.43 Tat

the edges of magnetic strings, the current increased by about 1.5

times under the mean electric field intensity of 4 kV/cm, which isthe ratio of the inter-electrode voltage to the spacing between the

discharge electrode and the collecting electrode. The current in-

creased by about 1.2 times under the mean electric field intensity of

4 kV/cm, when the magnetic flux density was 0.38 T at the edges of

magnetic strings.

However, as seen in Fig. 6, it was inconspicuous of the increase

of corona discharge current in the drift region magnetic field. As an

external cylinder magnet was employed, the discharge current

increased about 25% when the mean magnetic flux density was

0.015 T near the wire electrode.

In order to decrease the magnetic flux density near the dis-

charge electrode, the magnet rings were decreased. The discharge

current was almost unchanged when the mean magnetic flux

density was about 0 T in the ionization region. However, themagnetic flux density was stronger in the drift region under this

condition. It could be concluded that the corona discharge current

could not be enhanced by the Larmor movements of free electrons

in the drift region, i.e., the increase of the discharge current is not

relevant to the lengthening trajectory of free electrons in the wide

drift region.

The inter-electrode region can be divided into two parts as we

know, namely, the ionization region and the drift region. The ion-

ization region occupies only about 0.5% of the whole inter-electrode

Fig. 3. Schematic of experimental apparatus with drift region magnetic field. 1. HV

power supply, 2. HV divider, 3. cylinder electrode, 4. wire electrode, and 5. cylinder

magnet.

Fig. 4. Schematic of the magnetic lines of force and the electric lines of force in thedrift region magnetic field.

Fig. 5. Characteristic curves showing the discharge current as function of inter-elec-

trode mean electric field intensity for the negative corona discharges under different

magnetic field intensities in the ionization-region magnetic field experiment.

Fig. 6. Characteristic curves showing the discharge current as a function of inter-

electrode mean electric field intensity for negative corona discharges under differentmagnetic field intensities in the drift region magnetic field experiment.

J. Mi et al. / Journal of Electrostatics 66 (2008) 457462 459


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volume, while the drift region occupies about 95.5%. In the current

study, two different applications of the magnetic field have been

designed to produce different influences, respectively, on the ion-

ization region and drift region.

It is obvious that the increase of the corona discharge current is

mainly determined by the magnetic flux density in the ionization

region and is independent of the magnetic flux density in the drift

region. The increase of the discharge current is only due to the

enhanced ionization process in the small ionization region near

discharge electrode, and is not relevant to the lengthening trajec-

tory of free electrons in the drift region.

3.1. Influence of magnetic fields on the free electrons in the

ionization region

In the conventional negative corona discharges, free electrons

move along the electric lines of force due to the Coulomb forces of

the electric field. In the ionization magnetic field, however, the

magnetic lines of force lie perpendicular to the electric lines of force

in the vicinity of the wire electrode. The free electrons are acted

upon both Lorentz and Coulomb forces, hence Larmor movements

are formed.In order to elucidate this process, some correlative numerical

values of Larmor movements were estimated as follows.

The Larmor frequency of free electrons

f Bq2pm

(1)

where B is the magnetic flux density, q is an electronic charge, and

m is electronic mass. In the ionization-region magnetic field, f is

1.21010 rad/s when the magnetic flux density is 0.43 T at theedges of magnetic strings. The period of gyration T thus is about

0.8 1010 s.According to Ref. [15], we can also get the radius of ionization

region and the electric field intensity.

The radius of ionization region

a r0 0:03ffiffiffiffiffi

r0p

(2)

where r0 is the radius of the curvature on the discharge electrode.

So the radius of ionization region is about 7.1104 m.The electric field intensity can be estimated by using the Peek

formula in the ionization region [16]

E 3 106f

T0p

Tp0 0:03

ffiffiffiffiffiffiffiffiffiffiT0p

Tp0a

s !(3)

wherefis the coarseness of surface of the wire electrode,fz0.6; T0is the standard temperature, T0 273 K; p0 is the thermodynamicstandard state pressure,1.013

105 Pa; Tis the real temperature, K;

p is the real pressure, Pa.

Therefore, the electric field intensity is about 1.7 106 V/m inthe ionization region when the magnetic flux intensity is 0.43 T at

the edges of magnetic strings. Besides, when the collision is not

taken into account, the mean velocity can be calculated when a free

electron moves from the surface of wire electrode tothe edge of the

ionization region by the following two Equations:

qE$a 12

mV2 (4)

V 12

V (5)

where Vis the velocity of free electron at the edge of the ionizationregion, and V is its mean velocity, which is about 1.0 107 m/s.

Thus, it will take the free electron about 7.11011 s moving fromthe surface of the wire electrodeto the edge of the ionization region

when the magnetic flux density is 0 T. The moving time of free

electrons will increase in the ionization region when the ioniza-

tion-region magnetic field is applied, and the gyration time is at

least about 0.88 period.

And the radius of gyration

R mVBq

1:3 104 m (6)

According to the above analyses, the moving distance of free

electrons will increase at least by 8.2104 m in the ionizationregion when the free electrons move from the surface of the dis-

charge electrode. Therefore, the number of collisions will increase

to 215.2% and the mean energy of free electrons will decrease by

115.2% between two collisions (an electron free path) for these free

electrons under this condition. In conclusion, the discharge cur-

rents will be enhanced due to the exponential increase of collisions

for all the free electrons in the ionization region.

However, the trajectory of free electrons is very complicated

because of the collisions. In any case, it is certain that the trajectory

of free electrons substantially lengthened and the mean energy offree electrons decreases in the ionization region when the ioniza-

tion-region magnetic field is applied.

3.2. Influence of magnetic fields on the free electrons in

the drift region

In the drift region, the collisions could not promote ionization

because of the lower kinetic energy of free electrons. In addition,

the neutralizations could notoccur because only the negative space

charges (free electrons and negative ions) existed in the drift region

in the magnetically enhanced negative discharges. In the above two

experiments, the number of collisions between free electrons and

gas molecules also increased in the drift inter-electrode region forthe influence of the magnetic field. However, more free electrons

were attached by the gas molecules to form the negative ions in the

drift inter-electrode region. In a word, the charge concentration

increased and the drift velocity along the electric line of force for

both negative ions and free electrons decreased in these two

experiments.

It can also be explained why the increase of the discharge cur-

rents is not relevant to the lengthening trajectory of free electrons

in the wide drift region. We suppose that the output negative

charges from the ionization region are Q within per unit time (t).

Since both the neutralizations of charges and the ionizations are

inexistent in the drift region, all the charges Qshould come into the

collecting electrode in the same unit time according to the principle

of electric current continuity. Therefore, the discharge currentIQ/t, is a fixed value. It is obvious that the increase of the dis-charge currents is not relevant to the lengthening trajectory of free

electrons in the wide drift region, which is in accordance with the

experimental data. The discharge currents cannot be enhanced by

the lengthening trajectories of negative ions as well as that of the

free electrons in the magnetically enhanced negative corona

discharges.

In summary, the mechanism of the magnetic enhancement is

that the magnetic field could affect the ionization region. Therefore,

the corona discharge current was enhanced by the Larmor move-

ments of free electrons in the ionization region, and the space

charge concentration is enhanced in the whole inter-electrode

region. Moreover, the lengthening trajectories of free electrons and

negative ions cannot increase the corona discharge current in thedrift region. Remarkably, to increase the corona discharge current,



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it is important to install the permanent magnet near the discharge

electrode to induce a stronger magnetic flux density.

3.3. Optimum combination between electric field and

magnetic field

In the ionization-region magnetic field, the radius of gyration for

the Larmor movements increases with the mean electric field in-

tensity when the magnetic field remains unchanged. The moving

distance of a free electron consists of both the distance along the

electric line of force and the distance caused by Larmor movement

in an electron mean free path. When the magnetic field was fixed,

the moving distance of a free electron along the electric line of force

will increase with the inter-electrode electric field intensity in ev-

ery electron mean free path. That means the moving distances of

free electrons caused by Larmor movements will decrease with the

increasing inter-electrode electric field intensity in every electron

mean free path when the magnetic field was fixed. Therefore, the

relative increase (magnetically enhanced corona discharge to con-

ventional one) of the collision number between free electrons and

gas molecules should decrease with the enhancing electric field

intensity when the magnetic field remains unchanged. This tendsto restrain the enhancement of ionizations. However, the mean

energy of free electrons will increase with the electric field in-

tensity which tends to enhance ionization.

According to above analyses, it is predicted that the relative

increase of corona discharge current could have a maximum value

at a special point because the change of the relative increase of

collision number is in the opposite direction of that of the mean

energy of free electrons.

The characteristic curves (Fig. 7) were generated by analyzing

the data of the ionization-region magnetic field experiment,

showing the relative increase of discharge current as a function of

the inter-electrode mean electric field intensity for negative corona

discharges under different magnetic flux densities of 0.38 T and

0.43 T. Fig. 7 shows that the relative increase of the discharge cur-rent has a maximum value, which is accordant with our prediction.

The optimum combination between the electric field and the

magnetic field was obtained when the relative increase of the

discharge current is the maximum value. It greatly saves the energy

at this time.

The relative increase of discharge current would exceed 150%,

when the mean electric field intensity is about 4.2 kV/cm and the

magnetic flux density is 0.43 T. The characteristic curve (Fig. 8) was

generated by analyzing the data of the ionization-region magnetic

field experiment, showing the relative increase of current asa function of the magnetic flux density for negative corona dis-

charges under mean electric field intensity of 4 kV/cm, which is the

value for the practical operation of the ESP. According to Fig. 8, the

relative increase of the discharge current could attain the maxi-

mum value by using a proper magnetic field when the mean

electric field intensity is 4 kV/cm. The efficiency of the ESP will be

enhanced at the maximum value in the ionization-region magnetic

field because of the increased concentration of negative ions. The

optimum combination between the mean electric field of 4 kV/cm

and the magnetic field in the ionization region of about 0.43 T is

especially significant in the industrial applications of corona

discharges. Moreover, the relative increase of discharge current

could reach about 150%.

According to the mechanism of the magnetic enhancement, therelative increase of the discharge current is determined by two

factors: (1) The collision number between the free electrons and

the gas molecules in the ionization region; and (2) The mean

energy of free electrons. If the mean energy of free electrons is

beneath the minimum ionization energy of the gas molecules, most

of the gas molecules will not ionize. Under that condition, the

discharge current could not increase even if the collisions between

the free electrons and the gas molecules increase. In contrast, when

the number of the collisions decreases, the discharge current may

not increase even if the mean energy of free electrons exceeds the

minimum ionization energy of the gas molecules.

In the ionization region, besides elastic collisions between the

free electrons and the gas molecules, ionizations, excitations and

attachments are present at the same time. If the mean electric fieldintensity is fixed, the mean energy of the free electrons will

decrease when the magnetic field is used. Therefore, when the

collisions between the free electronsand gas molecules occurin the

ionization region, the probability of excitations and attachments

increases, whereas the probability of ionization collisions decreases

in the magnetically enhanced corona discharges. However, the

number of collisions between the free electrons and gas molecules

increases when the magnetic field is applied.

According to above analyses, the mean energy of the free elec-

trons decreases in the ionization region when the magnetic field is

applied, while the number of the collisions between free electrons

and gas molecules increases. Therefore, the optimum combinations

between the electric fields and magnetic fields may be as follows.

If the mean electric field intensity is fixed, the number ofcollisions between the free electrons and gas molecules will

Fig. 7. Characteristic curves showing the relative increase of current as a function of

inter-electrode mean electric field intensity for negative corona discharges underdifferent magnetic field intensities.

Fig. 8. Characteristic curves showing the relative increase of current as a function

of magnetic flux density for negative corona discharges under mean electric field of

4 kV/cm.

J. Mi et al. / Journal of Electrostatics 66 (2008) 457462 461


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increase with the magnetic flux density increasing, while the

mean energy of free electrons will decrease with the magnetic

flux density increasing. Initially, due to the increased number of

collisions (a decisive factor), the relative increase of the discharge

current grows with the magnetic flux density. Subsequently, the

relative increase of the discharge current attains a maximum

value when the magnetic flux density is a particular value. Then

the relative increase of the discharge current decreases with the

increase of the magnetic flux density because of the obvious

decreased mean energy of free electrons, which, in turn, becomes

the decisive factor. Thus the relative increase of the discharge

current would have a maximum value with the magnetic flux

density increasing.

Furthermore, if the magnetic flux density is fixed, the mean

energy of free electrons increases with the mean electric field in-

tensity in the ionization region, while the number of the collisions

between the free electrons and gas molecules decreases with the

mean electric field increasing. At first, due to the increased mean

energy of free electrons, which is a decisive factor, the relative in-

crease of the discharge current grows with the mean electric field

intensity. After that, the relative increase of the discharge current

attains a maximum value when the mean electric field intensity is

a particular value. Then the relative increase of the discharge cur-rent decreases with the increasing of the mean electric field

intensity because of the obvious decreased number of collisions,

which becomes decisive factor. Thus, there would be a maximum

value of relative increase of the discharge current with the mean

electric field intensity increasing.

4. Conclusions

In this paper, according to the research on the corona discharges

in the magnetic field, the following conclusions can be established:

(1) The mechanism of the magnetic enhancement is that the

magnetic field could affect the ionization region. Therefore, thecorona discharge current was enhanced by the Larmor move-

ments of free electrons in the ionization region, and the space

charge concentration is enhanced in the whole inter-electrode

region. Moreover, the lengthening trajectories of free electrons

and negative ions cannot increase the discharge current in the

drift region.

(2) The relative increase of the discharge current is much larger

when the permanent magnet is applied near the discharge

electrode than near the collecting electrode.

(3) When the magnetic field is fixed, the relative increases of the

discharge current for varied inter-electrode mean electric fields

have a maximum value in the magnetically enhanced negative

corona discharges.

(4) In order to reach the largest relative increase of the discharge

current under the inter-electrode mean electric field intensity

of 4 kV/cm for a practical ESP, the optimum magnetic field with

a magnetic flux density of about 0.43 T at the edges of magnet

strings should be selected.

(5) The relative increase of the discharge current is determined by

two factors. One is the collision number between the free

electrons and the gas molecules in the ionization region, and

the other is the mean energy of the free electrons. Moreover,

the changecharacteristic of the relative increase of the collision

number is in contrast to that of the mean energy of free elec-

trons, leading to optimum combinations between the electric

fields and the magnetic fields.

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