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Influence of magnetic fields on negative corona discharge currents
Journal of Electrostatics 66 (2008) 457–462
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
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
a b s t r a c t
Article history: Received 1 July 2007 Received in revised form 31 March 2008 Accepted 16 April 2008 Available online 28 May 2008
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 magnetically enhanced 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 magnetically 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 magnetically 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 electrostatic 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. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Magnetically enhanced Negative corona discharge Plasma
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 applications, 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 [7–10] indicated that Fuchs’ theory had successfully predicted the charging probability of fine
* Corresponding author. E-mail address: [email protected] (D. Xu). 0304-3886/$ – see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2008.04.010
particles. The experimental and mathematical study carried out by Reischl et al. [11] demonstrated that 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 agreement 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 advantageous 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
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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 ionizationregion 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 density to be higher in the ionization region than in the drift region. When the magnetic flux density was 0.43 T at the edges of magnetic 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 magnetic 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 conducted the research on the influence of the magnetic field on negative corona discharge current to further explore the mechanism of magnetically enhanced corona discharge. Only the magnetically enhanced negative corona discharges 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 experimental apparatus is shown in Fig. 1. The effective length of the stainless-steel wire electrode (4) was 10 mm and 0.5 mm in diameter. 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
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.
near the discharge electrode could be changed by increasing or decreasing the number of 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 delivering 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 magnetic 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 wire electrode 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 inside diameter of 56 mm and 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 the entire inter-electrode region could also be changed by increasing or decreasing the number of 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. 2. Schematic of the magnetic lines of force and the electric lines of force in the ionization-region magnetic field.
J. Mi et al. / Journal of Electrostatics 66 (2008) 457–462
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.
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Fig. 5. Characteristic curves showing the discharge current as function of inter-electrode mean electric field intensity for the negative corona discharges under different magnetic field intensities in the ionization-region magnetic field experiment.
As seen in Fig. 5, the corona discharge current was greatly enhanced by increasing the magnetic flux density in the ionizationregion magnetic field. When the magnetic flux density was 0.43 T at
the edges of magnetic strings, the current increased by about 1.5 times under the mean electric field intensity of 4 kV/cm, which is the ratio of the inter-electrode voltage to the spacing between the discharge electrode and the collecting electrode. The current increased 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 discharge 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, the magnetic 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 ionization region occupies only about 0.5% of the whole inter-electrode
Fig. 4. Schematic of the magnetic lines of force and the electric lines of force in the drift region magnetic field.
Fig. 6. Characteristic curves showing the discharge current as a function of interelectrode mean electric field intensity for negative corona discharges under different magnetic field intensities in the drift region magnetic field experiment.
supply (1) and the high voltage divider (2) in this experiment were accordant 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 magnetic 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 ionization 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 stronger magnetic field in the drift region than that in the ionizationregion magnetic field. The magnetic lines of force were also approximately perpendicular to the electric lines of force near the wire electrode. Clearly, the magnetic flux density gradually increased from the wire electrode to the cylinder electrode. 3. Influence of magnetic fields on the currents of negative corona discharges
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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 ionization 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 trajectory 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 ¼
Bq 2pm
(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 1.2 1010 rad/s when the magnetic flux density is 0.43 T at the edges 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
pffiffiffiffiffi a ¼ r0 þ 0:03 r0
(2)
where r0 is the radius of the curvature on the discharge electrode. So the radius of ionization region is about 7.1 104 m. The electric field intensity can be estimated by using the Peek formula in the ionization region [16]
sffiffiffiffiffiffiffiffiffiffi! T0 p T0 p E ¼ 3 10 f þ 0:03 Tp0 Tp0 a 6
(3)
where f is the coarseness of surface of the wire electrode, f z 0.6; T0 is the standard temperature, T0 ¼ 273 K; p0 is the thermodynamic standard state pressure, 1.013 105 Pa; T is the real temperature, K; p is the real pressure, Pa. Therefore, the electric field intensity is about 1.7 106 V/m in the 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 to the edge of the ionization region by the following two Equations:
qE$a ¼
V ¼
1 V 2
1 mV2 2
(4)
(5)
where V is the velocity of free electron at the edge of the ionization region, and V is its mean velocity, which is about 1.0 107 m/s.
Thus, it will take the free electron about 7.1 1011 s moving from the surface of the wire electrode to 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 ionization-region magnetic field is applied, and the gyration time is at least about 0.88 period. And the radius of gyration
R ¼
mV ¼ 1:3 104 m Bq
(6)
According to the above analyses, the moving distance of free electrons will increase at least by 8.2 104 m in the ionization region when the free electrons move from the surface of the discharge 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 currents 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 of free electrons decreases in the ionization region when the ionization-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 not occur 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 for the 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 currents 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 Q should come into the collecting electrode in the same unit time according to the principle of electric current continuity. Therefore, the discharge current I ¼ Q/t, is a fixed value. It is obvious that the increase of the discharge 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 movements 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 the drift region. Remarkably, to increase the corona discharge current,
J. Mi et al. / Journal of Electrostatics 66 (2008) 457–462
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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 intensity 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 every 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 conventional 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 tends to restrain the enhancement of ionizations. However, the mean energy of free electrons will increase with the electric field intensity 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 current 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
Fig. 7. Characteristic curves showing the relative increase of current as a function of inter-electrode mean electric field intensity for negative corona discharges under different 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.
field experiment, showing the relative increase of current as a function of the magnetic flux density for negative corona discharges 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 maximum 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, the relative 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 field intensity is fixed, the mean energy of the free electrons will decrease when the magnetic field is used. Therefore, when the collisions between the free electrons and gas molecules occur in 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 electrons 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 of collisions between the free electrons and gas molecules will
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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 intensity 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 increase 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 current 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, the corona discharge current was enhanced by the Larmor movements 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 change characteristic of the relative increase of the collision number is in contrast to that of the mean energy of free electrons, leading to optimum combinations between the electric fields and the magnetic fields.
References [1] M. Yamamoto, M. Nishioka, M. Sadakata, Sterilization by H2O2 droplets under corona discharge, J. Electrostat. 56 (2002) 173–187. [2] K. Yu, J. Zou, Y. Ben, Y. Zhang, C. Liu, Synthesis of NiO-embedded carbon nanotubes using corona discharge enhanced chemical vapor deposition, Diamond Relat. Mater. 15 (2006) 1217–1222. [3] J. Li, Z. Xu, Y. Zhou, Application of corona discharge and electrostatic force to separate metals and nonmetals from crushed particles of waste printed circuit boards, J. Electrostat. 65 (2007) 233–238. [4] K. Yanallah, S. Hadj Ziane, A. Belasri, Y. Meslem, Numerical modeling of ozone production in direct current corona discharge, J. Mol. Struct. 777 (1–3) (2006) 125–129. [5] M.M. Pauthenier, Moreau-Hanot, Charging of spherical particles in an ionizing field, J. Phys. Radium 7 (1932) 590–613. [6] B.Y.H. Liu, A. Kapadia, Combined field and diffusion charging of aerosol particles in the continuum regime, J. Aerosol Sci. 9 (1978) 227–242. [7] B.Y.H. Liu, D.Y.H. Pui, On unipolar diffusion charging of aerosols in the continuum regime, J. Colloid Interface Sci. 58 (1977) 142–149. [8] A. Hussin, H.G. Scheibel, K.H. Becker, J. Porstendorfer, Bipolar diffusion charging of aerosol particles – I: experimental results within the diameter range 4–30 nm, J. Aerosol Sci. 14 (1983) 671–677. [9] M. Adachi, Y. Kousaka, K. Okuyama, Unipolar and bipolar diffusion charging of ultra-fine aerosol particles, J. Aerosol Sci. 16 (1985) 109–123. [10] A. Wiedensohler, H.J. Fissan, Bipolar charge distributions of aerosol particles in high-purity argon and nitrogen, Aerosol Sci. Technol. 14 (1991) 358–364. [11] G.P. Reischl, J.M. Makela, R. Karch, J. Necid, Bipolar charging of ultrafine particles in the size range below 10 nm, J. Aerosol Sci. 27 (1996) 931–949. [12] A.V. Filippov, Combined field-diffusion charging of aerosol particles, J. Aerosol Sci. 27 (1996) 197–198. [13] D. Xu, J. Li, Y. Wu, L. Wang, D. Sun, Z. Liu, Y. Zhang, Discharge characteristics and applications for electrostatic precipitation of DC corona with spraying discharge electrodes, J. Electrostat. 57 (2003) 217–224. [14] D. Xu, L. Sheng, H. Wang, Y. Sun, X. Zhang, J. Mi, Study of magnetically enhanced corona pre-charger, J. Electrostat. 65 (2007) 101–106. [15] H.J. White, Industrial Electrostatic Precipitation, Addison-Wesley, Massachusetts, 1963, pp. 319–323. [16] X. Chen, L. Zou, Y. Huang, L. Ke, W. Chen, S. Huang, Assumption and verification of normal distribution model of electric field in wire-plate ESP, J. Wuhan Univ. Sci. Technol. 29 (4) (2006) 356–359.
Contents lists available at ScienceDirect
Journal of Electrostatics journal homepage: www.elsevier.com/locate/elstat
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
a b s t r a c t
Article history: Received 1 July 2007 Received in revised form 31 March 2008 Accepted 16 April 2008 Available online 28 May 2008
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 magnetically enhanced 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 magnetically 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 magnetically 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 electrostatic 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. Ó 2008 Elsevier B.V. All rights reserved.
Keywords: Magnetically enhanced Negative corona discharge Plasma
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 applications, 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 [7–10] indicated that Fuchs’ theory had successfully predicted the charging probability of fine
* Corresponding author. E-mail address: [email protected] (D. Xu). 0304-3886/$ – see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elstat.2008.04.010
particles. The experimental and mathematical study carried out by Reischl et al. [11] demonstrated that 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 agreement 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 advantageous 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
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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 ionizationregion 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 density to be higher in the ionization region than in the drift region. When the magnetic flux density was 0.43 T at the edges of magnetic 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 magnetic 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 conducted the research on the influence of the magnetic field on negative corona discharge current to further explore the mechanism of magnetically enhanced corona discharge. Only the magnetically enhanced negative corona discharges 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 experimental apparatus is shown in Fig. 1. The effective length of the stainless-steel wire electrode (4) was 10 mm and 0.5 mm in diameter. 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
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.
near the discharge electrode could be changed by increasing or decreasing the number of 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 delivering 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 magnetic 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 wire electrode 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 inside diameter of 56 mm and 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 the entire inter-electrode region could also be changed by increasing or decreasing the number of 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. 2. Schematic of the magnetic lines of force and the electric lines of force in the ionization-region magnetic field.
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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.
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Fig. 5. Characteristic curves showing the discharge current as function of inter-electrode mean electric field intensity for the negative corona discharges under different magnetic field intensities in the ionization-region magnetic field experiment.
As seen in Fig. 5, the corona discharge current was greatly enhanced by increasing the magnetic flux density in the ionizationregion magnetic field. When the magnetic flux density was 0.43 T at
the edges of magnetic strings, the current increased by about 1.5 times under the mean electric field intensity of 4 kV/cm, which is the ratio of the inter-electrode voltage to the spacing between the discharge electrode and the collecting electrode. The current increased 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 discharge 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, the magnetic 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 ionization region occupies only about 0.5% of the whole inter-electrode
Fig. 4. Schematic of the magnetic lines of force and the electric lines of force in the drift region magnetic field.
Fig. 6. Characteristic curves showing the discharge current as a function of interelectrode mean electric field intensity for negative corona discharges under different magnetic field intensities in the drift region magnetic field experiment.
supply (1) and the high voltage divider (2) in this experiment were accordant 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 magnetic 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 ionization 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 stronger magnetic field in the drift region than that in the ionizationregion magnetic field. The magnetic lines of force were also approximately perpendicular to the electric lines of force near the wire electrode. Clearly, the magnetic flux density gradually increased from the wire electrode to the cylinder electrode. 3. Influence of magnetic fields on the currents of negative corona discharges
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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 ionization 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 trajectory 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 ¼
Bq 2pm
(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 1.2 1010 rad/s when the magnetic flux density is 0.43 T at the edges 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
pffiffiffiffiffi a ¼ r0 þ 0:03 r0
(2)
where r0 is the radius of the curvature on the discharge electrode. So the radius of ionization region is about 7.1 104 m. The electric field intensity can be estimated by using the Peek formula in the ionization region [16]
sffiffiffiffiffiffiffiffiffiffi! T0 p T0 p E ¼ 3 10 f þ 0:03 Tp0 Tp0 a 6
(3)
where f is the coarseness of surface of the wire electrode, f z 0.6; T0 is the standard temperature, T0 ¼ 273 K; p0 is the thermodynamic standard state pressure, 1.013 105 Pa; T is the real temperature, K; p is the real pressure, Pa. Therefore, the electric field intensity is about 1.7 106 V/m in the 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 to the edge of the ionization region by the following two Equations:
qE$a ¼
V ¼
1 V 2
1 mV2 2
(4)
(5)
where V is the velocity of free electron at the edge of the ionization region, and V is its mean velocity, which is about 1.0 107 m/s.
Thus, it will take the free electron about 7.1 1011 s moving from the surface of the wire electrode to 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 ionization-region magnetic field is applied, and the gyration time is at least about 0.88 period. And the radius of gyration
R ¼
mV ¼ 1:3 104 m Bq
(6)
According to the above analyses, the moving distance of free electrons will increase at least by 8.2 104 m in the ionization region when the free electrons move from the surface of the discharge 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 currents 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 of free electrons decreases in the ionization region when the ionization-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 not occur 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 for the 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 currents 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 Q should come into the collecting electrode in the same unit time according to the principle of electric current continuity. Therefore, the discharge current I ¼ Q/t, is a fixed value. It is obvious that the increase of the discharge 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 movements 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 the drift 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 intensity 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 every 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 conventional 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 tends to restrain the enhancement of ionizations. However, the mean energy of free electrons will increase with the electric field intensity 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 current 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
Fig. 7. Characteristic curves showing the relative increase of current as a function of inter-electrode mean electric field intensity for negative corona discharges under different 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.
field experiment, showing the relative increase of current as a function of the magnetic flux density for negative corona discharges 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 maximum 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, the relative 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 field intensity is fixed, the mean energy of the free electrons will decrease when the magnetic field is used. Therefore, when the collisions between the free electrons and gas molecules occur in 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 electrons 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 of collisions between the free electrons and gas molecules will
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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 intensity 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 increase 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 current 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, the corona discharge current was enhanced by the Larmor movements 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 change characteristic of the relative increase of the collision number is in contrast to that of the mean energy of free electrons, leading to optimum combinations between the electric fields and the magnetic fields.
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