Inutake, M.

Kiwamoto, Y.

Saito, T.

Takahashi, T.

Tamano, T.

Tatematsu, Y.

Yoshimura, Y.

Physics of Plasmas

English

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Suppression of secondary electrons from an endplate of a tandem mirror by use of a biased mesh

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Suppression of secondary electrons from anendplate of a tandem mirror by use of a biasedmesh著者 犬竹  正明journal orpublication titlePhysics of plasmasvolume 2number 2page range 352-354year 1995URL http://hdl.handle.net/10097/47825doi: 10.1063/1.871439Suppression of secondary electrons from an endplate of a tandem mirror by use of a biased mesh T. Saito, Y. Kiwamoto, Y. Tatematsu, Y. Yoshimura, T. Takahashi, M. Inutake,a) and T. Tamano Plasma Research Center; University of Tsukuba, Tsukuba City, Iburaki 305, Japan (Received 1 August 1994; accepted 17 October 1994) Negative bias is applied to a mesh placed in front of an endplate of the GAMMA 10 tandem mirror [Phys. Rev. Lett. 55, 939 (1985)]. A bias voltage of around 10 V results in an increase of the potential difference by an order of kV in the end region. The increment is about two times the temperature of end-loss electrons and most of that stems from the sheath potential drop in front of the endplate. Provided that almost all the secondary electrons emitted from endplate are reflected, these results agree with the prediction of a potential model for the open magnetic field configuration [J. Phys Sot. Jpn. 61, 3153 (1992)]. 0 1995 American Znstitute ofPhysics. Secondary electron emission (SEE) from plasma facing materials strongly affects energy flow to walls as well as the potential distribution in the edge region.’ Moreover, SEE is an important factor for energy confinement in a tandem mir- ror because cold secondary electrons flow back to the con- finement region along magnetic field lines and replace heated electrons. Thus, examination of effects of SEE is one of key tasks in the study of mirror fusion. Theoretically, degradation of energy confinement due to SEE has been discussed in several papers2r3 and use of a biased mesh has been pointed out as one of the promising methods to suppress SEE. Also, an idea of a thermal dike has recently been proposed to re- duce the cold electron flow to the confinement region.4 How- ever, suppression of SEE has only been tested by using a picket fence of permanent magnets in a laboratory plasma.” This paper describes the first results of suppression of SEE by using a mesh placed on an endplate of GAMMA 10 (Ref. 6) and examines the dependence of the potential in the end region on the bias voltage. Figure 1 shows the potential profile expected in GAMMA 10. When electron cyclotron resonance heating at the plug is applied, an intense end-loss electron flux of hundreds of eV to several keV is generated7*’ and the endplate potential CD,, goes down.’ The end-loss electrons induce secondary electrons from the endplate.” The potential profile outside the mirror throat is predicted by a potential model including the experimental conditions.” The energy spectrum of the end-loss electrons is expressed by a Maxwellian of two temperatures T,, and TeH. The model takes account of the secondary electrons and the mag- netic field profile. Collisions are neglected and distribution functions of each species satisfy the Vlasov equation. The floating condition of the endplate determines the potential difference Aa as shown in Fig. 1. It has been confirmed that the experimental value of A@ is well reproduced by this model.12 The potential model gives the following expression to the end-loss electron flux re : lYe=Neo/~)“*[ exp( -T) - (“niJEP)exp( - BmyBEr +I]- (1) Here, NeO is the density of the end-loss electrons at the mir- ror throat and T, is the electron temperature. The magnetic field strengths at the mirror throat and at the endplate are denoted by B,, and BEP. The potential at the mirror throat measured from the endplate is represented by rBMP. Accord- ing to the model QMp increases with decreasing SEE coeffi- cient 7. The primary function of the mesh biasing is reduc- tion of the heat loss to the endplate by suppressing SEE. Thus, we have to examine the response of the potential dif- ference to the bias voltage. Moreover, mesh biasing confirms the effects of secondary electrons on the potential profile in an open system. The confinement region of the GAMMA 10 device con- sists of the central cell, two anchor cells, and two end mirror cells. Outside the confinement region, the end region ex- pands toward the endplate. The outer mirror throat of the end mirror cell connects the confinement region with the end region. The value of B, is 0.3 T and that of BEP is 0.01 T. The endplate consists of five annular rings.13 Each piece of the plates is made of stainless steel and connected to the machine ground through a high resistance. Negative voltage is applied to a mesh placed in front of the innermost plate (#l plate, 3650 cm*). A stainless steel mesh with 50 grids of 50 pm diameter wire per inch is used. The transparency of the mesh is more than 80%. The distance between the end- plate and the mesh is 2 cm. The bias circuit is floated from the machine ground and the reference of the bias is the end- plate. The potentials at the central cell a,, and at the barrier midplane QpB are measured by gold beam probes.14 The plug potential (Pp is evaluated from the energy spectrum of the end-loss ions. Two Langmuir probes shown in Fig. 1 are used to obtain the space potentials al and @o in the end region, The energy spectrum of the end-loss electrons is ob- tained with a multigrid energy analyzer called an LED (loss electron diagnostic). The response of the measured potentials to the mesh bias V, is shown in Fig. 2. Here, V, is the voltage between the mesh and the endplate. The bias circuit has a series resis- tance R, of 100 Sz and the circuit current I, is monitored. The supply voltage V, necessary to support VM is VM+Z,R, . On-axis values are plotted for Q’c, ap,, and Q>, . All the plotted potentials are referenced to the machine 352 Phys. Plasmas 2 (2), February 1995 1070-664W95/2(2)/352/3/$6.00 0 1995 American Institute of Physics Downloaded 06 Apr 2010 to 130.34.135.83. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp1 0 7 8 9 10 11 12 13 Z(m) FIG. I. Axial profiles of the magnetic field strength (dashed line) and the potential (solid line) in the end mirror cell and the end region. The potential profile in the end region corresponds to the calculated profile from the potential model. ‘The origin of the L axis is located at the midpiane of the central cell. The arrows except at the mirror throat indicate the positions of potential measurement. ground. The floating potential @a, promptly descends with ‘I’, and then saturates at V, of 20-30 V. Typical value of I, is 0.5 A at V, of 20 V. This behavior of @nP is understood if all the secondary electrons with a mean energy of around 10 eV are reflected to the endplate by the mesh. The floating potential descends to reflect end-loss electrons on way to the endplate. Consequently, the net current flowing to the end- plate is kept to be zero with reduced SEE. Contrary to the behavior of @nP, other potentials do not vary with V, . Figure 3 plots the axial potential profile along the magnetic field line which passes the #1 plate for three representative values of V, . The difference between @ , and Cp,, stands for the sheath potential drop (Psheath in front of the endplate and Fig. 3 indicates that most of the increment of A<f, = aP -G$r stems from the increase of Qsheath. From the viewpoint of the axial charge balance, only an increase of 1 ~“.I~~~~,‘.“,~‘.‘,‘.~‘,“” 0 10 20 30 40 50 60 v, (VI FIG. 2. Response of the potentials Q, (A), Qc (0). @a (Cl), @o (O), and @a, (V) to the voltage V, between the mesh and the endplate. The mesh voltage is negative to the endplate. Here, on-axis values are plotted by Qc, @a.and?i,. 0 -2 + 8 . . ,  ,  I .  .  .  .  8. 3 3 *  I .  t  I  *  9 10 11 12 13 14 Z (4 FIG. 3. Axial potential profiles for three representative values of V, . In this figure are plotted potentials on the magnetic field line which passes the #l plate. A @  is required. Therefore, it is also possible that both GP and @ ‘EP vary and results in the same A@. However, this is not the case in the present experiment. The potential mode1 predicts the response of the axial potential profile to variation of the SEE coefficient y. Figure 4 plots the calculated potentials corresponding to the plug, the probe position, and the endplate as functions of ‘y. In the mode1 the potential is referred to be zero at the mirror throat and normalized by the temperature T,, of the bulk compo- nent of the end-loss electrons. This model does not determine the potential as measured from the vacuum vessel. However, once we acknowledge the absolute value of the potential at each point for no bias as the initial one, the mode1 explains the observed response of the potentials to VM . Figure 4 states that the potential difference Aa t = (q,,-- qs) X T,, from the plug to the probe position is determined essentially independent of SEE. It is mainly determined from the dynamics of the end-loss ions and the end-loss electrons according to the rapid decrease of the 0 -1 2 5 -2 8 F -3 -4 O=.Ol -5 ' I I 0 0.2 0.4 Y  0.6 0.8 FIG. 4. The normalized potentials calculated by the model are plotted as functions of the secondary electron emission coefficient 7. The potential at the mirror throat is referred to be zero in the model. The difference qv,-WEP corresponds to A@/T,, and qs-qa, denotes @rhelth/TeL, where, A@=@P-@E, and @)Eheath=@o-@aP. Phys. Plasmas, Vol. 2, No. 2, February 1995 Letters 353 Downloaded 06 Apr 2010 to 130.34.135.83. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jspy = 0.7 0 ~~~~'~~,.'~~~~'~~*~'.~~~ 0 10 20 30 40 50 v&g 09 FIG. 5. Normalized potential difference A@/T,, is shown as a function of vM. magnetic field strength outside the mirror throat. The second- ary electron density is much smaller in the confinement re- gion than at the probe position and hence the potentials in the confinement region are determined independent of SEE from the endplate. Thus the plug potential @, does not vary with V, . On the other hand, the model provides the total differ- ence AQ, and the apportion between A@, and asheath. The only way to meet all the above restrictions is as shown in Fig. 3. Next we compare the measured increment of AQ, with that of the calculation. Figure 5 plots ALIT,, as a function of V,. The value of T,, does not change very much with V,. The normalized potential difference quickly increases with V,,, from around 3 and then saturates at about 5. The quantity AQlT,, compares with ‘PP-TnP shown in Fig. 4, which also varies from 3 to 5 with decreasing ‘y. Thus, the experimentally observed value is consistent with the calcu- lated value if all the secondary electrons are reflected at VM larger than 20-30 V and y is regarded as zero. In this experiment only the #l plate is covered by the mesh and SEE from the outer plates is not controlled. The measured floating potentials of the outer plates do not vary when a bias voltage is applied to the mesh. This means that the predominant factor determining the potential profile along each magnetic field line is the axial dynamics of end- loss particles. This also supports the application of the model which takes only the axial dynamics of the particles into account. The increase of AQ, reduces the loss power density W to the endplate. The potential model gives the following expres- sion of W: W=Tj(2Ti+eA@)+2r,Te. (2) The ion flux is denoted by Ti and the electron flux I’, is given by Eq. (1). Contribution of the secondary electrons is neglected. Equation (2) is essentially the same formula as given in Ref. 3. However, the end-loss electrons have two components in GAMMA IO and T, should be replaced by Terf=( 1 - P)T~L+ PTe,y. Here, /3 is the flux fraction of the higher temperature component. The difference between W with bias and that without bias is Here, 89 is the increment of A@. When SEE from the end- plate is suppressed, the relation lYi = I’e,bias holds. From the experiment, e&I? is nearly equal to Tew and lYe,o = (2-3) x re,biass Hence the positive ion term is masked by the negative electron term. Because qp,, increases by 8$, reduction of lYe can be estimated by using Eq. (I) if N,-, and T, do not change. In fact. N,, and T, may vary by mesh biasing. Moreover, the end-loss electrons have two compo- nents. Therefore, we use the experimentally observed values. The total electron flux measured by the LED decreases from 8.7X 10e4 A/cm2 to 4.2X10e4 Alcm2. The value of T,, shghtly increases from 0.5 to 0.6 keV. Thus SW is estimated to be about 0.37 W/cm2. If we simply multiply this vaIue by the area of the #l plate, decrement of the loss power to the #l plate is 1.3 kW per one end. On the other hand, the power V, I, dissipated in the bias circuit is equal to 70 VX0.5 A=0.035 kW, which is much less than the above value. A negatively biased mesh suppresses secondary elec- trons emitted from the endplate and increases the sheath po- tential drop in front of the endplate. The potential drop re- duces the loss power to the endplate with a very low cost of bias power. Though a material mesh may work only in an experiment with low power density, the present study dem- onstrates the effectiveness of suppressing backward flow of colder electrons for decreasing eiectron heat load to end walls. For larger experiment, thermal dike, e.g., is a possible candidate to be studied next.‘5P*6 alPermanent address: Department of Electrical Engineering, Faculty of En- gineering, Tohoku University, Sendai, Japan. ’ P. C. Stangeby, in Physics of Plasma- Wall Interactions in Controlled Fu- sion, NATO AS1 Series B-131, edited by D. E. Post and R. Behrisch (Plenum, New York, 19841, p. 41. ‘L. S. Hall, Nucl. Fusion 17, 681 (1977). 3G. D. Porter, Nucl. Fusion 22, 1279 (1982). ‘T. Ohkawa, Kakuyugo-Kenkyuu (J. Plasma Fusion Res.) 64, 305 (1990). ‘C. Chart, H. Bewley, N. Hershkowitz, and I. R. Dekock, Nucl. Fusion 22, 105 (1982). 6M. Inutake, T. Cho, M. Ichimura, K. Ishii, A. Itakura, I. Katanuma, Y. Kiwamoto. Y. Kusama, A. Mase, S. Miyoshi, Y. Nakashima, T. Saito, A. Sakasai. K. Sawada, I. Wakaida, N. Yamaguchi, and K. Yatsu, Phys. Rev. Lett. 55, 939 (1985). ‘T. Karyia, T. Saito, Y. Kiwamoto, T. Cho, H. Sugawara, T. Kondoh, A. Mase, A. Itakura, and S. Miyoshi, Phys. Fluids 31, 1815 (1988). sY. 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Saito, I. Katanuma, Y. Yoshimura, and T Tamano. PhyH. Plasmas 1, 3986 (1994). 354 Phys. Plasmas, Vol. 2, No. 2, February 1995 Letters Downloaded 06 Apr 2010 to 130.34.135.83. Redistribution subject to AIP license or copyright; see http://pop.aip.org/pop/copyright.jsp

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Suppression of secondary electrons from an endplate of a tandem mirror by use of a biased mesh

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