The submitted manuscript has been authored by a contractor of the U. S. Government under contractt DE-AC5-96R24464. Accordingly, the U. S. Government retains a non-exclusive, royalty free license to publish or reproduce the published form of this contribution, or allow others to do so, for U. S. Government purposes... Acceleration of electrons in the near field of lower hybrid frequency grills ** ** M.Goniche('), J.Mailloux*, Y.Demers*, D.Guilhem, J.H.Harris, J.T.Hogan, P.Jacquet*, P.Bibet, P.Froissard, G.Rey, F.Surle, M.Tareb Centre d' 6tudes de Cadarache Association Euratom-CEA F- 1318 Saint Paul-lez-Durance, France * Centre canadien de fusion magn6tique 184 BouLLionel-Boulet, Varennes, Qukbec, Canada, J3X 1s 1 **Oak Ridge National laboratory, Oak Ridge, Tennessee, USA (I) Present adress : JET Joint Undertaking, Abingdon, Oxfordshire, OX14 3EA, UK Presented at the the 22nd European Physical Society Conference on Plasma Physics and Controlled Fusion, Kiev, Ukraine, 17-21 June 1996
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Acceleration of electrons in the near field of lower hybrid frequency grills * ** ** M.Goniche(l), J.Mailloux*, Y.Demers, D.Guilhem, J.H.Harris, J.T.Hogan, P.Jacquet*, P.Bibet, P.Froissard, G.Rey, F.Surle, M.Tareb Centre d' Ctudes de Cadarache Association Euratom-CEA F- 1318 Saint Paul-lez-Durance, France * Centre canadien de fusion magnctique 184 Boul.Lione1-Boulet, Varennes, QuCbec, Canada, J3X 1 S 1 **Oak Ridge National laboratory, Oak Ridge, Tennessee, USA (I) Present adress : JET Joint Undertaking, Abingdon, Oxfordshire, OX14 3EA, UK 1. Introduction On Tore Supra, during lower hybrid (LH) current drive experiments, localized heat flux deposition is observed on plasma facing components such as the guard limiters of the LH grills [ 11 or any object which is magnetically connected to the LH launching waveguides : modular low-field side limiters, ion cyclotron heating antennas, inner first wall. Similar observations have been made on the divertor plates and limiters of TdeV [2]. In particular, by alternating the rf powers of the 2 grills of Tore Supra, it was shown that the heat flux on the tiles of the guard limiters is related to the local electric field but not with the convective power [3]. We present here a model of acceleration of electrons in the near field of LH antennas. Results of this model are compared to experimental results. 2. Model We will consider the trajectory of the guiding center along the field lines, in a 1D model. Electrons are supposed to be driven only by the oscillating electric field and any electrostatic fields are neglected. In the near-field approximation, waves of amplitude E,, and phase (pn excited by each individual waveguide n do not interfer and the particle responds successively to the discrete values of the electric field when travelling along the array of waveguides. This assumption is valid only for a very thin layer (few mm) at the antenna aperture. In such conditions, the equation of motion of an electron traveling from one side of a waveguide to the opposite side is simply --- d2z - (-e) En. sin(ot + cpn) where E,, and (p, are the amplitude and the phase of the electric dt2 m field excited by the waveguide n. If only the fundamental TEOl mode is considered, E, and (pn are constant and integrating twice the equation of motion leads to a set of non-linear equations which
4 can be easily numerically solved to obain the final speed and the phase of the electron with respect of the wave. Starting from an initial random phase and a Maxwelian velocity distribution (E=25eV), the final energy distribution is obtained by a nw-step iterative method.where nw is the number of waveguides in a row. 3. Results of computation Let us consider first the ideal case where the phasing A@ between adjacent waveguides is constant (A@=9Odeg.) and the amplitude is the same for the n=32 waveguides (E= 1.3 and 4.5 lo5 Vim). This corresponds to a perfect antenna with no reflection from the plasma. It is convenient to use the normalized velocity v*=2v/ob (o/2n: is the rf frequency and b the waveguide width). The velocity distribution function f(v*) is the superposition of the initial distribution (corresponding to the non-accelerated electrons) and a much wider distribution function (Figure 1). For the low electric field case, electrons are accelerated up to 6 ev (v*=o. 1 l), but for the high electric field case, the distribution function is even more widening and the final energy can reach 4.2 kev (v*=.3). For the 2 cases, the mean energy of the accelerated electrons is repectively 12 and 62 ev. The latter case can be compared to a plasma-loaded antenna case : for a Tore Supra shot, for which 3.2 MW was launched with 1 of the 2 antennas, the electric field distribution is calculated from the rf measurements achieved at the input of the antenna and the coupling code SWAN. For 1 of the waveguide rows, the mean electric field is 4.5 15V/m (standard deviation 1.1 lo5 V/m) and the mean phasing is 93 deg. (standard deviation 36 deg.). It can be seen that the velocity distribution is modified with respect of the ideal case : mean and maximum energies of the accelerated electrons are reduced to, respectively, 435 and 22 ev (v*=.22). The near-field approximation is strictly valid only at the antenndplasma interface. Further in the plasma some smoothing of the electric field must occur. In order to evaluate the effect of the sharpness of the E-function on the acceleration process, the discrete values of the electric field En were linearly linked up on a length d. For d >lmm, the mean acceleration of the electrons falls off rapidly, Accordingly, the high N// content (23<N//<lOO), which is related to small scale features, decays (Figure 2).
1.5.2 1 f.1.5.1.2 V*.3 Figure I. Velocity distribution function for direrent electric fields 1 d (mm) * Figure 2. Effect of Erfgradiant on mean energy and high N// content) 3 3 Experimental results On Tore Supra, heat flux on plasma facing components connected to the array of waveguides was evaluated in a wide range of RF powers (2-5 MW). In these experiments, the 2 LH antennas were 4 cm from the LCFS and a vertical limiter at the bottom of the vessel was set 2.5cm behind the LCFS in order to intercept low convected flux from the plasma. For a specific value of qa (qa=6), both antennas are connected to this limiter (ion-drift direction, L,,=15m) and, in addition to the 4 hot spots observed on each LH gard limiter, a superposed array of 2x4 hot spots are found from analysis of the IR images. For the 4 hot spots on the antenna 2 limiter and for 2 hot spots on the vertical limiter which were identified to be connected to antenna 2 only, the measured heat flux is plotted as a function of the average calculated electric field. On the same graph, the mean enegy of the electrons is also plotted for the 4 rows (Figure 3). Lower values on vertical limiter is due to the grazing angle (3-5 deg.) of the field lines with the surface of this limiter, wheras on the antenna limiter the field lines strike the surface with larger angle (15-45 deg). Effect of plasma and SOL densities on the total power lossed by this mechanism has been studied in details on TdeV. For a given plasma configuration (single-nul diverted plasma, qa=3.9), the plama 19-3 density was varied between 2 and 6 1 m. In this configuration, with a fixed distance of 1.5cm between the antenna and the separatrix, the antenna is connected to specific divertor plates. A good correlation is found between this edge density and the total losses on the connected plates (Figure 4). This correlation is much weaker when considering the plasma density. On Tore Supra, total losses have been measured by thermographic and calorimetric measurements : when the plasma density 19-3 ranges betwwen 1.5 and 3.5 1 m, losses are in the 1-2 % range No edge density were available 18-3 for these shots but for similar plasma conditions, density in the.5-1. 1 m range have been measured.
12 1-8 - 4 - P b Ant.2-Row2 Ant.2-Row3 iant.2-row4 Heat Flux I LimiterLw n -- # CI, 6 4 - n4 4 I : * I 1 I I l*l 3 E(kV/cm) 5 LE F i e l d Figure 3. Measured heatflux and calculated acceleration A A A TdeV A M A 2 1 2 3 4 Ne (1**18m-3) 5 Figure 4. EfSect of the density at the antenna on the total losses 4. Conclusion Acceleration of thermal electrons occurs in the near field of LH antennas up to a few kev. This acceleration arises from small scale variation of the electric field or, equivalently, high N// content of the launched spectrum. Semi-analytical model shows that the acceleration vanishes when no power with N,, >23 is available. These accelerated electrons provide a heat flux on connected components : For typical electric field strength (4 kv/cm), the normal heat flux in the flux tube is estimated to be 4 MW/m2 from thermographic measurements. For such conditions, calculations taking into account self-consistant effect of the accelerated electrons lead to the same heat flux. The fraction of power coupled to the thermal electrons increases with the electronic density at the antennna aperture and losses bellow 3% are measured when this density is lower than 1 1'8m-3. For the next step machine, calculations show that the increase of density at the antenna due to the increase of frequency from 3.7 to 5. Ghz should enhance the heat flux by only 1%. References [l] M.Goniche et al., IAEA conference, Seville, 1994 [2] J.Mailloux et al., J.of Nucl.Mat., 1996 [3] J.H.Harris et al., Controlled Fusion and Plasma Physics 1995