Long Pulse EBW Start-up Experiments in MAST

The non-solenoid start-up technique reported here relies on a double mode conversion for electron Bernstein wave (EBW) excitation. It consists of the mode conversion of the ordinary mode, entering the plasma from the low field side of the tokamak, into the extraordinary (X) mode at a mirror-polarizer located at the high field side. The X mode propagates back to the plasma, passes through electron cyclotron resonance and experiences a subsequent X to EBW mode conversion near the upper hybrid resonance. Finally the excited EBW mode is totally absorbed at the Doppler shifted electron cyclotron resonance. The absorption of EBW remains high even in cold rarefied plasmas. Furthermore, EBW can generate significant plasma current giving the prospect of a fully solenoid-free plasma start-up. First experiments using this scheme were carried out on MAST [V. Shevchenko et al, Nuclear Fusion 50, 022004 (2010)]. Plasma currents up to 33 kA have been achieved using 28 GHz 100kW 90ms RF pulses. Recently experimental results were extended to longer RF pulses showing further increase of plasma currents generated by RF power alone. A record current of 73kA has been achieved with 450ms RF pulse of similar power. The current drive enhancement was mainly achieved due to RF pulse extension and further optimisation of the start-up scenario.


I. INTRODUCTION
Non-solenoid plasma current start-up is a critical issue in spherical tokamak (ST) research because of lack of space for a shielded central solenoid. Various techniques have been proposed and developed in order to avoid a central solenoid in future ST devices [1][2][3][4][5]. In this paper, we report on the electron Bernstein wave  The plasma start-up method deployed here has been proposed in [7,8] and first experiments were described in [1]. The method relies on the production of lowdensity plasma by RF pre-ionization around the fundamental EC resonance (ECR) with an ordinary (O) mode, incident from the low field side of the tokamak. Then the O mode is reflected back by a grooved mirror-polarizer incorporated in a graphite tile on CR. Polarization of the reflected beam is rotated by 90° to convert to the extraordinary (X) mode. The launched O-mode Gaussian beam is tilted to the midplane at 10° and hits the CR at the midplane as illustrated in fig. 2a Black colour at the end of EBW rays indicates the power deposition zone. a) poloidal crosssection: rays absorbed predominantly above the midplane; b) in the absorption zone EBW rays develop N || > 0 above the midplane and N || < 0 below. Note, about 5 times higher than usual density n e (0) = 1.5·10 18 m -3 is depicted. In this case the ECR and UHR layers are well separated while preserving the main features of EBW propagation.
The X mode reflected from the mirror-polarizer propagates back into the plasma and hits the ECR layer predominantly above the midplane. The X mode propagating nearly perpendicular to the magnetic field has very small absorption at the fundamental EC resonance within a wide range of plasma parameters typical for tokamak. Thus almost all the X-mode power passes through the ECR and experiences a subsequent slow X to EBW mode conversion (MC) near the upper hybrid resonance (UHR). Finally the excited EBW mode is totally absorbed before it reaches the ECR, due to the Doppler shifted resonance. Modelling shows that only a small fraction of the injected RF power (~2%) is typically absorbed as the O and X modes in start-up plasmas, while the main part is converted into the EBW mode. The absorption of EBW remains high even in cold rarefied plasmas. Indeed, one can estimate absorption using a simple analytical formula obtained within a global wavedynamical treatment of MC processes [9]. It gives good agreement with numerical simulation within the range of parameters typical for start-up plasmas.
where τ is an optical thickness, R is a major radius of the plasma, k = ω RF /c is a wave vector, c is a speed of light ω pe and ω ce are a plasma frequency and an electron cyclotron frequency respectively. For the MAST start-up parameters it can be simplified even further: where ݊ ଵ ଼ is an electron density in unit of 10 18 m -3 . Finally the absorption coefficient A can be estimated as usual: One can see that absorption is very close to 100% within a wide range of densities and it is independent of plasma temperature. Furthermore, EBW can generate significant plasma current (if EBW absorption is localised predominantly above or below the midplane to gain a directionality with respect to the magnetic field) during the start-up phase giving the prospect of a fully non-inductive plasma start-up [10].
The described schematic has natural limitations. The first limit comes from accessibility requirements. The plasma must be transparent for the O mode and the deflection of the O-mode beam due to refraction should not exceed the size of the mirror polariser at CR. That means that the plasma must be well under-dense for the RF frequency ω RF injected into the plasma, i.e ω RF 2 >> ω pe 2 , or equivalently n e << n e cut-off (ω RF ) with n e cut-off = 9.7·10 18 m -3 for 28 GHz discussed here. The second limit comes from the lower density case. If the density is so low that the following inequality is valid: where T e is an electron temperature and m e is an electron mass, then the X-B MC does not take place and the X mode passes through the plasma [9]. During the RF breakdown phase this low density limit is usually quickly exceeded and the gas puff needs to be controlled to avoid the plasma reaching over dense condition.
The usual relativistic resonance condition must be satisfied by electrons near the fundamental EC resonance to provide efficient interaction with the waves, is the relativistic factor, v⊥ and v || are the components of the electron velocity perpendicular and parallel to the magnetic field, and k || = N || ·k is the component of the wave vector k parallel to the magnetic field B and N || is the corresponding refractive index. Even for start-up plasmas with relatively low electron temperature the Doppler downshift of ECR is important in the case of EBWs because while approaching the resonance they can develop very large k || . In the presence of high power RF heating the electron distribution function may develop high energy tail then relativistic effects can also be important.
The EBW wave vector is essentially perpendicular to the UHR layer so ܰ usually B T >> B P hence k || ≈ k T +k P B P /|B|, where k T and k P are the toroidal and poloidal components respectively. At their origin EBWs have k vector almost perpendicular to the UHR layer resulting in |k P B P /|B|| >> |k T |, except for in the vicinity of the midplane. Therefore the sign of k || is mainly determined by the sign of k P B P /|B|. As seen in fig. 2b as EBW propagates towards the EC resonance, k || is developed further due to poloidal plasma inhomogeneity. This effect determines a different sign of k || above and below the midplane. Moreover, k P B P /|B| changes sign if the plasma current is reversed and remains unchanged if the toroidal field is reversed [10]. EBW rays propagating close to the midlane usually do not contribute significantly to the current drive because their N || experiences oscillations between small positive and negative values which result in a close to zero net current after averaging over the rays around the midplane [11,12]. A detailed theoretical study of EBW propagation in tokamak plasma can be found in [13] and in particular near the midplane [14 ].

II. LONG PULSE EXPERIMENTS
The original hardware was significantly upgraded since first experiments [1]  have also confirmed good focusing of the launched beam as the "hot" spot observed with an infrared camera was well centred at the mirror-polarizer and its angular dimensions agreed with the beam radius of 80 mm. Total resistive losses on the invessel mirrors were estimated to be less than 5%. seen in Fig. 2a  in the present MAST geometry is about 700 V/cm [15]. This interval was identified as a free electron density build-up phase. Then the SRD signal dropped suddenly and exponentially down to less than one tenth of its previous value within 0.1 -0.2 ms indicating the onset of the EBW breakdown phase.
From this moment a strong growth of plasma density, EC emission and plasma current was observed. This behaviour of signals was reproduced in the whole range of experiments discussed below providing evidence that typically more than 95% of the injected power was absorbed by the plasma. Single pass absorption close to 100% was reported for other start-up experiments with high field side X-mode launch [16].  In the second shot #28941 shown in fig. 3 Bv is partly set before the RF pulse.
Then Bv is ramped up to a higher value during P6 vertical kicks. Then all fields remain constant from 0.12 s through the whole duration of the RF pulse until 0.29 s.
As in the previous shot Ip monotonically increases until the end of RF injection. In both shots plasma current reaches the same value at 0.19 s but in the second one it was achieved with smaller radial field but higher Bv ramp-up. The smaller radial field is required to produce the same vertical shift because Bv is smaller. Monotonic Ip growth until the end of RF pulse indicates that saturation has not been achieved with this value of Bv. Immediately after the end of the RF injection Ip starts to decrease and at a rate which then increases dramatically when the P4 coil current is switched off and the plasma loses equilibrium.  were used to conduct beam-tracing [17] for O and X-mode propagation followed by EBW ray-tracing [18] and Fokker-Planck simulations [19] discussed in the section III.  [20]. For comparison of different experiments a dimensionless current drive (CD) efficiency is more commonly used [21]: the major radius in meters, P W is the RF power in W, and T keV is the local temperature in keV. This result is close to the dimensionless efficiency obtained in short pulse EBW start-up experiments [1].
The plasma image taken at the end of the RF pulse is shown in fig. 7. The plasma has a clear toroidal structure with elongated poloidal cross-section.
Unfortunately due to low density in this shot Thomson scattering measurements of plasma density and temperature profiles were not possible.  Interestingly, all experimental points fit a linear dependence of generated plasma current versus RF power injected into the plasma. At least this dependence seems to be valid within the range of RF power available in the experiments reported in this paper. In the present launcher set-up the RF breakdown occurs at power levels exceeding ~10kW. So the curve should start at the 10kW point followed by a stronger than linear dependence until it gradually joins the line presented in fig. 8.

III. EXPERIMENTS WITH VERTICAL MODULATION
It was predicted in [11] and experimentally confirmed in [10] that the EBW power deposition location with respect to the plasma midplane is crucial for the EBW current drive (CD) direction. A special experiment was conducted to verify the CD mechanism responsible for the current generation in the start-up scenario under discussion. To change the vertical localisation of EBW power deposition within the plasma is impossible with the existing launching system because it was designed with reference to the mirror-polariser position. The entire RF launching system was carefully pre-aligned to provide efficient mode conversion on the mirror-polariser which is fixed at the midplane on the central rod. However it is possible to move the plasma midplane with respect to the machine midplane by applying radial magnetic fields produced by P6 coils. That would allow an experimental test of the effect of the EBW power deposition location on CD efficiency and direction. Such behaviour can be understood from the following consideration. In a nondisturbed position shown in fig. 2 all EBW power is absorbed above the midplane.
This power produces CD in the co-direction. When the plasma was moved up while the RF beam remained fixed some fraction of the EBW power will be deposited below the plasma midplane causing CD in a counter-direction. That will result in a reduction of the total CD and hence a reduction in plasma current. Conversely when plasma moves down the fraction of the power deposited above the plasma midplane becomes larger resulting in the increase of plasma current. These experiments qualitatively prove the EBW CD mechanism in this start-up scenario.
The MAST vessel (see Fig.1   210 eV and about 500 ms for T e = 420 eV which is close to the experimentally observed values. Here we used the same notation as in [22] where ‫ݓ‬ This discrepancy can be attributed to the fact that simulations started with Maxwellian distribution while in the experiment the counter-CD was applied to the electron distribution which had already developed a high energy tail due to the previous co-CD. Obviously, more detailed measurements in a wider parameter range are necessary in order to clarify all the physics involved in EBW start-up. There is no evidence of run-away electrons in the plasma generated by the described method.

V. CONCLUSIONS
Improvements, upgrades and associated testing of the high power 28 GHz system used for the MAST EBW start-up have been performed as collaborative research between ORNL and CCFE. RF power injected into the vessel was of the same level as in previous experiments [1] but the RF pulse length was increased by a factor of 5 (up to ~0.5 s). These long pulse EBW start-up experiments on MAST have more than doubled the previously achieved plasma current levels. Closed flux surfaces were clearly observed indicating that tokamak like equilibrium was established during the EBW start-up phase. The response of the plasma current to vertical modulation of the plasma midplane demonstrated that the current was driven by EBWs. However modelling predicts a smaller total current generated by EBWs but a stronger response of the plasma current to the vertical modulation than observed in the experiments. A power scan indicates that the plasma current generated after closed flux surfaces formation depends linearly on the RF power injected. ECE measurements during EBW start-up support the hypothesis that plasma current is predominantly carried by supra-thermal electrons with energies about 27keV.