The lower hybrid current drive system for steady-state operation of the Vulcan tokamak conceptual design

Fusion Engineering and Design 87 (2012) 215–223

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The lower hybrid current drive system for steady-state operation of the Vulcan tokamak conceptual design Y.A. Podpaly ∗ , G.M. Olynyk, M.L. Garrett, P.T. Bonoli, D.G. Whyte Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA, USA

a r t i c l e

i n f o

Article history: Available online 29 December 2011 PACS: 28.52.−s 28.52.Fa 52.55.Fa 52.55.Rk Keywords: Tokamak Steady-state Fusion development Lower hybrid Current drive

a b s t r a c t The steady-state current drive system for the Vulcan tokamak concept has been designed, taking into account requirements of high field, small size, and high operational wall temperature (B0 = 7 T, R0 = 1.2 m, Twall > 800 K). This lower hybrid current drive system allows steady-state operation by utilizing high field side launch, high RF source frequency (8 GHz), and dedicated current drive ports. An iterative MHD and current drive solver is used to determine the ideal launching spectra and location to assure strong single pass absorption. It is found that with nominal Vulcan operational parameters (ne ≈ 4 × 1020 m−3 , Te ≈ 2.8 keV, Ip = 1.7 MA, PLHCD = 19.8 MW) bootstrap currents of ∼70% and lower hybrid current drive efficiencies of 1.16 × 1019 A W m−2 could be achieved. The optimized solution yielded advanced tokamak profiles with q values on-axis above 2. A conceptual design of the system is presented, which takes into account space, power, cooling, and launched spectrum requirements. The system is found to be compatible with the vacuum vessel design and requires cooling power of <1 MW per waveguide bundle. © 2011 Elsevier B.V. All rights reserved.

1. Introduction The Vulcan tokamak conceptual design [1–4] (Vulcan hereafter) is intended to allow plasma–material interaction studies in reactor-like conditions. The reactor is projected to have a divertor heat flux of ∼10 MW/m2 and high inner wall (>800 K) temperature. In order for Vulcan to properly simulate reactor-relevant plasma bombardment of materials, the device must operate for plasma-facing-material–relevant time scales that can range from picoseconds (sputtering) to years (neutron-induced material modification and gross erosion), which requires the consistent use of steady-state non-inductive current drive. The Vulcan target parameters from [1] are shown in Table 1. Non-inductive methods, either self-generated or external, of driving current are required for steady-state operation of tokamak fusion reactors. Bootstrap current – self-generated current due to pressure gradients and the orbits of trapped particles in the plasma – provides some of the steady-state current without the use of the √ central solenoid. The bootstrap fraction scales as fB ∝ ˇp , where  is the inverse aspect ratio and ˇp is the ratio of plasma pressure to poloidal magnetic field pressure. Therefore, advanced tokamak profiles (q > 1 and high ˇt , ˇp ) are expected to have high self-driven

∗ Corresponding author. Tel.: +1 617 253 0025; fax: +1 617 253 0627. E-mail address: [email protected] (Y.A. Podpaly). 0920-3796/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2011.12.001

current, which can ease the operation of such tokamaks. The fraction of plasma current that is self-generated can be significant, but bootstrap should not be 100% of the current, in order to maintain plasma control. The amount of current required beyond the bootstrap current must be provided by other sources. Numerous methods of generating this current exist, including tangential neutral beam injection, ion cyclotron range of frequencies fast wave current drive (ICRF FWCD), electron cyclotron current drive (ECCD), and lower hybrid current drive (LHCD). Although all of the aforementioned methods are used in present-day devices, LH current drive is particularly well-suited to the current drive requirements of Vulcan where efficient offaxis current generation is needed. The densities and temperatures expected in Vulcan are ne ∼ 4 × 1020 m−3 and Te  ∼ 3 keV. Under these conditions, existing neutral beam injection (NBI) sources operating at ∼100 keV would have a beam penetration distance characterized by an e-folding length of ∼8 cm, making them unsuitable for driving current even at r/a ∼ 0.5 in Vulcan (a = 30 cm). It is important to note, however, that significant increases in beam energy are planned for the ITER device, where 1 MeV sources are being developed, but these are not considered in the Vulcan design. Furthermore, for Vulcan plasmas with hot plasma-facing components and high electron density, it is expected to have low Zeff ∼ 2 and relatively low Te , thus leading to a neutral beam current drive efficiency of approximately 0.62 × 1019 A W−1 m−2 [5,6], which is below the level predicted for LHCD. Electron cyclotron

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Table 1 Target Vulcan parameters projected to produce SOL/PMI/PFC divertor similarity to a reactor using the “P/S” scaling. Projections done using 0-D analysis [1]. Parameter

Value

Plasma major radius (R) Plasma minor radius (a) Plasma elongation () Plasma triangularity (ı) On-axis toroidal field Bt Plasma current (Ip ) Areal power density (P/S) Safety factor (q* ) Average density (ne ) Average temperature (T e )

1.2 m 0.3 m 1.7 0.7 7T 1.7 MA 1 MW m−2 3.0 4.0 × 1020 m−3 2.7 keV

Overall, the plasma physics constraints can provide contradictory requirements on the system frequency and n . In general, hot plasmas with low density, low n (current drive efficiency scales as 1/n2 ), and high launch frequency are ideal for LHCD. The value of n is desired to be as low as possible, in order to keep LHCD efficiency high, as long as the waves are still accessible to the core of the plasma. The constraints such as accessibility, avoiding instabilities, and maintaining high current drive efficiency are summarized below. One of the results of the extension to the electromagnetic plasma dispersion relation, assuming reactor-like scalings (ωpe /ωce ∼ ωpi /ω ∼ n ∼ 1 and ωpi /ωci ∼ ω/ωci ∼ ωce /ω ∼ n⊥ ∼ (mi / me )1/2 1) [12], is that there develops an accessibility condition



current drive has the benefit of straightforward coupling of power and localized current generation. On the other hand, the efficiency of ECCD is significantly reduced due to particle trapping at r/a > 0.5, which is generally the desired location for non-inductive current profile control in Vulcan; in [7] for Te = 4.3 keV and ne = 3.7 × 1019 m−3 the approximate current drive efficiency at midradius is 0.4 × 10−19 A W−1 m−2 which is below calculated LHCD efficiencies and, given the low density of that simulation, can be taken as a best case scenario for Vulcan. Current drive with fast magnetosonic waves (FWCD) has also been shown to be feasible; however, this scheme would also suffer from particle trapping in off-axis current drive applications. Thus, the most natural use of FWCD in the Vulcan conceptual design is to provide on-axis seed current, especially in discharges with high shear reversal. It is also worth noting that if sources were to be developed at ≈320 GHz, ECCD could also be used for on-axis seed current generation. Lower hybrid waves, however, have the attractive property that they damp efficiently on electrons at v /vte >3 and can be used for off-axis current generation with minimal adverse effects from magnetic trapping [8]. For example, at low density and intermediate temperatures, LHCD has been observed to have global efficiencies as high as 2.5 × 10−19 A W−1 m−2 [9]. Thus the preferred choice for off-axis current generation in Vulcan is LHCD. It is interesting to note that other non-inductive advanced tokamak reactor designs [10] have relied on LH waves for efficient off-axis current drive with other methods for on-axis generation. Therefore, while obtaining reactor-like pulse lengths, Vulcan will simultaneously test reactorrelevant current drive technology and plasma physics.

1/2

n2 > K⊥



+ −KA2 /K

1/2 2

2 /ω2 − ω2 /ω2 , K⊥ = 1 + ωpe ce pi 2 2 −ωpe /ω . This generally requires

where

(2) 2 /ω ω , KA = ωpe ce

and

an increase in the launched K = n in order to minimize conversion of the LH wave to the electromagnetic fast wave and subsequent propagation to the plasma edge, where the wave reflects from a cut-off. However, the accessibility requirement is reduced by higher local magnetic field since the RHS of Eq. (2) decreases monotonically with ωce . Because LHCD relies on electron Landau damping, there is an additional constraint on n : quasilinear Landau damping dominates

2.1. Physics considerations

at nc  7.0/T (keV)1/2 [11]. This relation means that LHCD works better at higher temperatures where the hot electron tail is able to damp higher proportions of the energy from the wave. At extremely high plasma temperatures, however, the wave would not be able to penetrate to the core of the plasma and would primarily drive current at the plasma edge. Conversely, at low temperatures, this effect will force one towards higher n , decreasing current drive efficiency. A more detailed discussion of this damping and LHCD modeling in the TdeV tokamak is presented in [13]. It is important to note, however, that slow waves undergoing conversion to the fast mode are still absorbed through a combination of parallel electron Landau damping and transit time magnetic pumping and drive current with reduced efficiency. Furthermore, it has been found experimentally [14] that as the frequency drops below 2ωLH , the power in the LH “pump” wave couples nonlinearly to modes that damp in the plasma edge, through a process known as the parametric decay instability (PDI) [15]. This effect adds the requirement of keeping the launched wave frequency above the parametric decay frequency 2ωLH . Overall, the efficiency of lower hybrid current drive is calculated to be approximately  = 1.17/n2 R0 n20 , where n20 is the plasma

Lower hybrid current drive functions by Landau damping of the driven electrostatic wave on the fast electron distribution in the plasma. Most waves can be used for this mechanism, but some are more effective given their accessibility to the core plasma and ability to damp on the fast electron distribution. The dispersion relation for the slow wave lower hybrid branch in the electrostatic cold plasma approximation is

LHCD ≡

2. Lower hybrid current drive

 2

ω =

2 ωLH

k 2 m 1+ 2 i k me

 (1)

2 = ω2 /(1 + ω2 /ω2 ) and ω2 ˝2 . The parameter k where ωLH pe ce ce pi is the parallel wave number and is directly related to the parallel refractive index n = ck /ω. Due to the conservation of the parallel electric field across a material boundary, the wave n does not change except from geometric effects. In warm and hot plasmas, the dispersion relation is more complicated and is discussed in detail in [11].

density in units of 1020 m−3 [12]. This relation shows that lower n is greatly favored for current drive, in conflict with the accessibility and temperature requirements. LHCD efficiency is typically normalized to density and major radius, in order to remove the gross −1 n−1 e R0 dependence, which is present in most CD mechanisms. The LHCD efficiency is thus defined as: ILHCD R0 ne PLHCD

(3)

2.2. Optimizing the poloidal launch location Currently, most lower hybrid current drive systems utilize standard radial diagnostic ports, which are generally located at the outboard midplane. This location has unfavorable magnetic geometry and bad curvature, which generates large intermittent particle and energy fluxes radially outward due to E × B drift (i.e. away from the confined plasma towards larger R and the launching structures). This plasma transport, both quiescent and intermittent, can cause material erosion and thermal damage to the launcher. Despite this,

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In addition, a Vulcan-specific problem is the physical dimensions of the Vulcan secondary vacuum vessel through which the lower hybrid wave guides must pass before entering the primary vacuum vessel [4]. The waveguides must lie adjacent to the hot primary vessel without compromising their physical structure. In addition, arcing in the launcher mouth and waveguides must be avoided, which places a limit on the amount of power and the maximum frequency that can be directed through the system. These constraints mean that it is beneficial to minimize the length of waveguide exposed to the hot primary vacuum vessel environment. High LHCD frequency also forces the use of small waveguides, complicating the construction of the launcher mouth. On the other hand, the high field side has a toroidally continuous plasma wall acting as the limiter, which protects the launcher mouth from damage, rather than the discrete limiters used by present LFS LHCD systems. Finally, an increase in launched n forces a decrease in the width of the waveguides, so lower launched refractive index can improve the power handling of the waveguides. 3. Numerical modeling of non-inductive scenarios Fig. 1. Comparison of the high and low field side flux values through the inner and outer scrape off layers (SOLs) on Alcator C-Mod at a density of 1.0 × 1020 m−3 . Figures compare pressure, current, and flow velocity through the SOL between a lower single null (LSN) and balanced double null (BDN) discharge. Note that on the HFS in BDN geometry, the jsat  value approaches zero giving a fictitiously high fluctuation rate versus the LFS rate. Data courtesy B. LaBombard [16].

present devices are able to utilize LHCD because the LH systems operate only for times short enough that the fluxes do not greatly impair intra-shot reliability. The erosion and damage problems can be greatly alleviated by positioning the launching structure at the high field side of the tokamak where the good curvature of the plasma lowers these fluxes and makes the plasma less intermittent. Indeed E × B drift tends to move the plasma towards higher R, i.e. away from the launchers. Fig. 1 compares the plasma behavior on the low and high field sides of the plasma on Alcator C-Mod [16]. The figure shows edge pressure (Fig. 1a), probe currents (Fig. 1b), and particle flux (Fig. 1c) in two different geometries (LSN and BDN). It is seen that by creating a plasma with two magnetic X-points (locations with zero poloidal field), a configuration known as “balanced double null” (BDN), the edge/scrape off layer (SOL) pressure and flow velocities on the high-field side are markedly lowered, reducing the possible damage to the launcher due to decreased plasma transported heat flux. This is caused by the fact that the bad curvature low-field side, which is the dominant location for power to be released into the SOL in a tokamak, is magnetically disconnected from the inner SOL. This makes LH coupling much easier, since the local density at the launcher mouth is readily controlled with simple movement of the inner gap between the high-field side wall and this quiescent scrape off layer – the plasma region just outside the last closed flux surface, with a sharp radial decay in density. The inner SOL heat flux is also greatly reduced in BDN, due to its isolation from the low-field side, significantly reducing the power handling requirements and the possibility of thermal damage to the launching structure. This geometry isolates the high field side SOL reducing the local heat flux. Furthermore, there is an advantageous gain in wave behavior when launching from below the midplane on the high field side: the wave refractive index rises before entering the plasma, so it is possible to launch at a value below the core refractive index cutoff value and still remain accessible throughout the plasma. This behavior is discussed in more detail in Section 3 and the theoretical basis of this advantage is discussed in Section 5.

The complexity of lower hybrid wave propagation and deposition in the toroidal geometry makes analytic solutions intractable, so modeling codes are required. In this work, the ACCOME [17] code, an iterative, free-boundary MHD solver with accompanying neutral beam, lower hybrid, and bootstrap current modules, was used. It self-consistently solves for plasma shape, current drive, and bootstrap current. Transport is not considered by the code, so profiles of temperature and density are supplied by the user as functions of flux surface. Volume-averaged temperatures can change due to equilibrium modifications as the MHD solver iterates with the current drive packages. Throughout the modeling process, Alcator C-Mod [18] profiles were scaled to Vulcan 0-D predictions in order to use empirically derived profiles. Alcator C-Mod profiles are chosen because of the device’s ability to create steady H-mode profiles and high magnetic fields and densities. The Vulcan poloidal field coils were taken to be inside the toroidal field magnets and were checked to confirm that they fit within the device’s physical dimensions. Modeling cases were run until profiles and calculated plasma shapes had realistic magnetic topologies for the types of discharges being examined. The n spectra and waveguide launch position were then changed in order to find the most desirable launch conditions and magnetic geometries. This process was then iterated due to the coupling of the lower hybrid system and the plasma parameters. In reality, any ray that does not damp on its first pass into the plasma can lose a significant fraction of its power due to parasitic losses in the scrape-off layer when it propagates back out to the plasma edge [19], which is an undesirable effect. In ACCOME, however, the edge of the plasma is treated as a near perfect reflector. Therefore, any simulation which had a ray contact the edge with more than 10% of the original beam power not already deposited (i.e. strong single pass absorption) in the core was discarded. Numerical stability of the runs was also confirmed by examining the difference between successive iterations. 3.1. Modeling results The lower hybrid system was simulated using three equally poloidally spaced rays that cover the extent of the launcher mouth as defined by the physical constraints discussed in Section 4. The LHCD source frequency was chosen to be 8.0 GHz, to remain above the 2ωLH PDI limit. The profile shapes of plasma temperature and density were chosen to match Alcator C-Mod H-mode profiles, but

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Fig. 2. Assumed profiles for Vulcan as scaled from Alcator C-Mod H-mode profiles.

are scaled to match the Vulcan 0-D analysis [1]. These profiles are shown in Fig. 2. The input power required to maintain the desired P/S of 1 MW m−2 is 19.8 MW. Various launch positions and refractive indices were simulated. A summary of some of the tested parameters is presented in Table 2, where the core plasma conditions are set for PMI similarity using the P/S scaling rules from [2]. These rules require full noninductive scenarios with the constraint of global heating power density (P/S ∼ 1 MW/m2 ), q ∼ 3, reactor-like B ∼ 6–7 T, and sufficiently high plasma density to achieve edge/divertor plasmas with credible heat exhaust solutions which closely match those in eventual reactors. Optimization of CD efficiency is therefore required, and is obtained by the choice of frequency and launch position. By optimizing the launch position to the plasma geometry and taking advantage of the beneficial n behavior on the HFS of the tokamak, it is possible to effectively launch the LHCD rays through the most favorable path to the plasma core, minimizing edge losses. This is seen in Table 2 through the increase in efficiency as the launcher mouth is moved in the negative vertical direction. As the optimized position was approached, the launcher was redesigned to take account for the lower launched n , so the vertical size of the launcher was decreased in the final simulation. The bootstrap fraction is seen to decrease with lower vertical position because the LHCD is driving more current overall in the plasma while the bootstrap current is remaining mostly unchanged, thus decreasing the bootstrap fraction. The optimized ACCOME simulation, which corresponds to the last row of Table 2, is discussed in more detail below. In the case presented here, Te  = 2.8 keV and ne  = 3.9 × 1020 m−3 . 3.1.1. Optimized high-field side launch The rays from the launcher are shown in Fig. 3, and the n versus the accessibility limit for each ray is shown in Fig. 4. The behavior of the refractive indices often has an early rise after launch which allows launching at lower values of the refractive index. The lowest section of the launcher could have a lower launched n in order to have higher efficiency, however to standardize launcher mouth shapes, it was chosen to keep all launched n identical for the final optimization. In this case, the bootstrap current is calculated to be 1.27 MA and the lower hybrid current is calculated to be 0.48 MA, leading to a total plasma current of 1.8 MA and a bootstrap fraction of 71%. This current exceeds the target current in the 0-D optimization in [1], and it serves as a proof of principle in establishing non-inductive scenarios at reactor-relevant q* and edge similarity. It will also be possible to over-drive the current in order to recharge the central solenoid, which would then be available for temporary inductive

Fig. 3. ACCOME-calculated lower hybrid ray tracing of the optimized case (launched n = 2.2,  = 1.16 × 1019 A/(W m−2 )) in high field side launch. Red circles refer to 10% decreases in original ray power. Note that the elongated tail in the top beam case actually carries very little power, since >90% of it has already been lost in the plasma. Flux surfaces drawn as they are solved self-consistently by ACCOME. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

CD if required due to unscheduled loss of LH. With these values of current, the global efficiency is 1.16 × 1019 A W−1 m−2 . The r/a profiles of the various currents are shown in Fig. 5. This deposition profile shows significant off-axis non-inductive

Fig. 4. n evolution as the launched rays (see Fig. 3) travel through the plasma, for (a) top ray, (b) middle ray, (c) bottom ray. The red solid line represents the actual n and the blue dashed line represents the local accessibility limit. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Table 2 Various HFS lower hybrid launch positions for optimization of current drive with divertor similarity (Table 1). Negative positions refer to launching below the midplane. Launch positionscm from midplane

Launched n

A W−1 m−2

fB %

Ip MA

ICD MA

−15, − 20, − 25 −20, − 25, − 30 −25, − 30, − 35 −25, − 30, − 35 −30, − 35, − 40 −35, − 40, − 45 −38.6, − 43.0, − 46.4

3.0, 3.0, 3.0 3.0, 3.0, 3.0 3.0, 3.0, 3.0 2.5, 2.5, 2.5 2.3, 2.3, 2.2 2.3, 2.3, 2.2 2.2, 2.2, 2.2

0.830 × 1019 0.865 × 1019 0.852 × 1019 0.967 × 1019 0.898 × 1019 0.934 × 1019 1.16 × 1019

80.9 80.9 80.7 77.2 80.3 80.3 70.7

2.04 2.04 1.97 1.82 2.05 2.05 1.80

0.390 0.390 0.382 0.415 0.403 0.403 0.527

current and the presence of large bootstrap currents, particularly at the edge due to the H-mode pedestal. The small beam-driven current is only to prevent a numerical instability on axis for the Grad–Shafranov solver; the neutral beam driven current drive is an order of magnitude below the lower hybrid current, so it is not expected to greatly affect the solution’s applicability. The ACCOME simulation employs an NBI system for central current drive. Since an NBI system capable of driving core current at these densities is not practical (as discussed earlier), the NBCD should be considered to be a proxy for a generic on-axis current drive system, such as fast-wave ICRF, which could generate the small level of current necessary for control of the central q. Furthermore, the JT-60U tokamak has demonstrated the ability to run without on-axis current drive [20], so there exists the possibility of running without onaxis current drive. Nevertheless, there is a strong likelihood that an on-axis mechanism for driving current will be required to prevent current holes in the Vulcan plasmas. The q-profile created by this deposition is shown in Fig. 6. The qprofile is greatly elevated from the typical on-axis minimum of q = 1, and has a highly sheared shape, leading to possible internal transport barriers [21] and improved transport and confinement over what was assumed in the 0-D analysis. The avoidance of sawteeth and 2/1 tearing modes, which are known to degrade confinement and cause disruptions, would be greatly beneficial to steady-state operation.

Fig. 6. ACCOME-calculated q profile for the nominal case with high-field-side launch LHCD (see Figs. 3 and 4). Note that as J → 0 at the core, the profiles of current density are smoothed, so the q-profile and the current density profile do not appear to represent each other perfectly.

3.1.2. Optimized low-field side launch For comparison, it has also been attempted to optimize lowfield side launch with the same core plasma parameters. Plots of this case are shown in Figs. 7 and 8. The low-field-side launch position was found to be best at 22 cm above the midplane and

Fig. 5. Current distribution in the nominal case. The largest LH driven current is significantly off axis; there is negative current drive at the outer most plasma locations because of the negative launched n waves from a non-fully-continuous LH launcher. The negative current drive is countered by the strong bootstrap current from edge pressure gradients. Note that the code applies slight smoothing in the radial direction of the neutral beam and LH currents in order to help with the stability of the Grad–Shafranov solver. This correction is only noticeable at the axis.

Fig. 7. Optimized low-field side launch ray profiles for the same core plasma as Fig. 3. Red circles correspond to 10% reduction in beam power. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

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Fig. 8. Low-field side refractive index n of (a) the top beam, (b) the middle beam, and (c) the bottom beam from the low field side. The solid red line shows the ray’s n and the dashed blue line is the local accessibility condition. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

n = 2.9. The LH efficiency in this case is 0.69 × 1019 A W−1 m−2 ; 59% as efficient as the high-field side launch. This confirms that there are significant physics advantages to operating at HFS launch, which are discussed in detail in Section 5. It is important to note that for this high density case, most locations of LFS launch, including those centered at the outer midplane were incompatible with the Vulcan requirements (i.e. they did not have strong single-pass absorption, exhibited rays that reflected multiple times from the boundary, or required overly high n ). For this reason, it is judged that the LFS launch is significantly less robust than the HFS launch. 3.1.3. Non-inductive scenario with low density and bootstrap fraction The previous sub-sections examined a case at the highest density likely envisioned for Vulcan P/S similarity. In that case, the H-mode profiles provide substantial bootsrap current. Therefore, non-inductive scenarios at the opposite end of the likely density range were also explored to see if non-inductive scenarios are feasible using HFS launch with low bootstrap fraction. In this subsection, the average density is 1.3 × 1020 m−3 and the temperature is 2.4 keV; profiles of this case are shown in Fig. 9. Modeling results of ray propagation and resulting current profiles are shown in Figs. 10 and 11, respectively; the launch positions are slightly

Fig. 9. Assumed profiles for Vulcan as scaled from Alcator C-Mod H-mode profiles in the low density case.

Fig. 10. Ray tracing as calculated by ACCOME for the scenario with lower density and bootstrap fraction. Red circles correspond to a 10% reduction in beam power. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

modified from the high density scenario to re-optimize the simulation. In this case, the total current was 1.66 MA and the bootstrap fraction was 12%. Over 80% of the current in this situation will be driven by the lower hybrid system, and the current drive efficiency is 1.13 × 1019 A W−1 m−2 . Note that the current deposition profiles show that the current is mostly deposited close to the magnetic axis, so even though there is significant non-inductive current, it is behaving like a solenoid-driven device. It was calculated that the on-axis q value is below one, so the profile is no longer that of an advanced tokamak, and the sawtoothing instability will exist. This exercise, therefore, informs us that robust non-inductive scenarios can be accomplished over a wide range in density and bootstrap fraction in Vulcan using HFS launch.

Fig. 11. Current distribution in low density, low bootstrap fraction case.

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Fig. 12. Vulcan LHCD concept illustration, with LH waveguide and launcher shown in the optimized position on the high-field side of the tokamak.

4. Conceptual design of LHCD system The design of the system was implemented in parallel with the modeling, requiring an iterative approach. A conceptual illustration of the system inside the Vulcan vacuum vessel concept is shown in Fig. 12. The design shown is for the case of a launcher operating at 8.0 GHz and with a launched parallel refractive index of 2.2. Klystrons were chosen as the microwave source since they allow phasing of relative waveguides and are the currently used sources on many major devices for LHCD. Transmission from the klystrons to the inside of the secondary vacuum vessel is accomplished using WR-112 waveguides. Access to the central column of the vessel is provided by the double vacuum vessel design of Vulcan [4]. Once the waveguides approach the hot primary vacuum vessel, they are reduced to a smaller size, in order to allow launching the smallrefractive index waves, and go through a four-way splitter into the launcher mouth. The smaller waveguides are based on the WR-112, with a reduction in the short dimension to 3.26 mm. Each launcher is composed of a phased waveguide array made up of 16 rows and 4 columns, with 1 mm septa between the small waveguides. This results in a launcher size of 6.8 cm by 12 cm (∼80 cm2 ) at the plasma edge. The amount of power that can be fed through each of these launcher structures before breakdown depends on the conditioning of the launcher: approximately 370 kW for weak conditioning, 620 kW for extensive conditioning [22]. Since the system is to be operated above 800 K, extensive conditioning is assumed. This leads to a power density in the launcher mouth of ≈77 MW/m2 . Since the required power as estimated by the 0-D analysis is 19.8 MW, at least 32 separate launchers are required (with a total surface area coverage of ∼0.25 m2 ; while the total inner column surface area is ∼6.2 m2 ). These launchers would be distributed toroidally on the inner wall, and it is conceivable to phase them relative to each other to improve the directionality as a whole. Power losses in the launching system are a significant source of heating and can result in waveguide physical failure. Estimates of power losses are shown in Fig. 13. These estimates assumed a copper waveguide with high-strength nickel alloy support structures for physical rigidity. Total power losses were approximately 1 MW over the entire launching system, which is within the Vulcan cooling abilities since the divertor will be required to exhaust at least 10 MW. It is conceivable that a passive–active multijunction (PAM) system [23] can be used in order to allow the passive section of the launcher to act as a coolant duct for helium gas. There is detailed work being undertaken to operate such lower hybrid launchers and to understand their thermal behavior [24,25]. A detailed design of the coolant system will need to be explored prior to construction, and it will likely be the same as the divertor and first wall

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Fig. 13. Estimated power losses in average lower hybrid system waveguides from klystron to plasma.

coolant, described in [4], which uses helium gas to prevent damage to the plasma-facing components. The divertor system is capable of exhausting ∼10 MW m−2 over the divertor strike points and should, thus, be able to handle the heat load from the LHCD system as well. In order to minimize the size of the waveguides and prevent thermal shorts between the primary and secondary vacuum vessels, the four-way splitter is positioned between the primary and secondary vacuum vessel. This system makes it possible to use a minimum number of waveguides throughout most of the length of the tokamak and then split to the launcher mouth and still achieve proper launching parameters. The Vulcan 4-way splitter concept is based upon the Alcator C-Mod lower hybrid splitter [26,27]. Finite element method simulations were used to develop an optimized conceptual design for the waveguide transformer and splitter structure. To split the power into four poloidally-spaced launcher guides, apertures are cut into the narrow dimension of the guide, spaced one guide wavelength apart. A three-quarter wavelength short is positioned at the splitter termination for matching. The launcher is optimized for equal power split among guides. A phase-shifting structure is added to the lowest two launch guides to ensure even poloidal phasing and equal power coupling to the plasma for a sub-midplane, high field side launch position. An example finite element simulation of this splitter is shown in Fig. 14, which launches fixed n waves at different poloidal locations. Given that the LH launching system is currently foreseen to be an integral part of the primary vacuum system, and given the small size of the gap between the primary and secondary vacuum vessels in Vulcan, in-situ repair of the LH launchers will likely be difficult, if not impossible. It is seen in the modeling, however, that the 32 launchers will overdrive the tokamak past the required current for plasma operations. This overdrive allows some of the launchers to be damaged with little to no detrimental effects on steady-state plasma operation. If the number of damaged launchers starts to negatively affect plasma performance, either a more conservative plasma operation can be used, or the primary vacuum vessel would have to be removed as described in [4], and the launcher would be replaced or repaired outside of the secondary vacuum vessel. A final issue that has not been addressed in detail in this conceptual study, but would need to be studied prior to construction is the location of the vacuum windows in the design. This is a critical issue in order to prevent arcing in the lower hybrid waveguides and also to prevent the windows from sustaining damage from the plasma, increasing the reflection in the launcher. It is known that the vacuum windows in reactors must have no line-of-sight access to the plasma, allow a significant non-vacuum length to control arcing, withstand arcing at the window face itself, and prevent the nonvacuum region from reaching the ω = ωce layer where breakdown in the gas will be problematic [29].

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Robust single-pass absorption required at high density is primarily determined by the ray trajectories in the poloidal plane (e.g. Fig. 3), which is set by the evolving and competing radial and poloidal group velocities, i.e. ∂ω/∂ kr and ∂ω/∂ k respectively. These group velocities are determined from the dispersion relationship (Eq. (1)) and the definitions k2 = kr2 + k2 + kϕ2 and k =  /|B|. In addition, to examine core propak bˆ  + kϕ bˆ ϕ where bˆ j = B j ∼ k2 = k2 ω2 /ω2 , which gation, we make the simplification that k2 = ⊥



pe

is a good approximation at small radial distances from the edge plasma and wave cutoff. This results in the following expressions for group velocities:



vg,r ≡

2 ωpe ∂ω ∼ =− 1+ 2 ∂kr ωce

vg, ≡

∂ω ∼ = ∂k



1+

2 ωpe 2 ωce

−1

ω3 kr 2 k2 ωpe

−1 ω

1 ˆ b k 

(4)

(5)

and the ratio of radial to poloidal group velocity is

vg,r ∼ ω2 kr 1 =− 2 vg, ωpe k bˆ 

Fig. 14. Finite element code [28] simulation of the four-way splitter designed for the Vulcan LHCD system. Electric field is color-coded (red represents electric field out of the page and blue represents electric field into the page) and is shown in units of V/m. The phase shifter on the lower channels maintains launched phase across the four launching waveguides. Total input power is 38 kW. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

The worst-case scenario for power density handling for the windows would be placing them directly at the launcher mouth, where they would have to handle approximately 7.7 kW cm−2 of power density. Windows that can handle that power density, however, have been designed and operated [29,30] implying that this is not an unsolvable issue. Another concern for the windows that must be analyzed in the future is the high-temperature operation of the vacuum vessel, which could cause degradation of the ceramic windows if they are exposed to the high temperature region. Since the full engineering design of the LHCD system has not been completed, the window location is not specified, but, given the above-mentioned concerns, a likely location is in the large waveguide region of the system, some distance from the primary vacuum vessel. 5. Discussion 5.1. Physics advantage of HFS launch The numerical modeling described in Section 3 clearly shows the benefits of using high-field side launch as compared to low-field side launch. It is appropriate, however, to examine the underlying causes of this benefit. The choice of HFS launch would seem to make the engineering of the launchers more difficult simply due to the smaller area on the inside of the torus and decreased physical access for maintenance. These issues of access are the reason that present LHCD systems utilize low-field size launch, typically from the outer midplane (e.g. C-Mod, Tore Supra). Coupled with the high power density typical of LH frequencies (∼70 MW m−2 ), the double vessel design of Vulcan fortunately appears to allow HFS launch. However, if one extrapolates past Vulcan to a steady-state reactor or volume neutron source then the HFS launch must be incorporated into the blanket/shield design from the very onset, and therefore one desires a high level of confidence in the physics advantages.

(6)

Eq. (6) immediately informs us to the difficulty of LHCD at high density: as density and plasma frequency increase, the rays will trend towards propagating more poloidally than radially inward (negative vg,r ) propagation. Based on the launch location, this tends to increase the chance of the rays approaching the boundary, with the possibility of edge collisional damping [19]. This trend of poor central penetration exacerbates the difficulty of external current drive at high density, which intrinsically decreases as ne . By examining Eqs. (4)–(6), however, one can develop an optimized strategy to overcome this difficulty at high ne ∼ ωp : 1. Increasing the launch frequency since the radial-to-poloidal group velocity ratio, vg,r /vg, , increases as the square of frequency (Eq. (6)). 2. Decrease k ∼ n , since this monotonically increases vg,r /vg, (Eq. (6)). If waves are launched at the accessibility limit (Eq. (2)) for reasons of CD efficiency, this can only be accomplished by launching at higher ωce and therefore a higher B field. 3. Eq. (5) informs us that the direction of poloidal propagation will always be in the negative poloidal direction for this helicity (or counter-clockwise as plotted in Fig. 3) for co-current drive because the sign of k must always be opposite to the sign of bˆ  . For a shaped, high-density plasma such as Vulcan, an obvious strategy based on geometry is to move the launcher to the lower left quadrant since this provides the best starting trajectory to “aim” the rays to the mid-radius, which is the optimal location for damping. 4. Decrease the magnitude of the local poloidal field bˆ  normalized to total field since this increases vg,r /vg, (Eq. (6)), i.e., launch waves in regions of large flux expansion. In a diverted plasma, this can be achieved by launching near poloidal null locations. This set of strategies is precisely the “recipe” that has been applied for Vulcan via the numerical simulations. The launch frequency has been increased to the maximum practical value presently available, and following strategic points 2–4, the optimal poloidal launch location is on the HFS close to the X-point, i.e. in the location shown in Fig. 3. This results in a nearly purely radial penetration of the rays in the early portion of their trajectories; a situation different than that of the LFS launch of Fig. 7, where their earlier trajectories have little radial component and, in fact, swing outward in major radius due to the plasma shape. An additional benefit of HFS launch from the lower half of the plasma results in the n upshift which provides improved accessibility.

Y.A. Podpaly et al. / Fusion Engineering and Design 87 (2012) 215–223

Based on this simple analysis, and validated by the numerical results, there is not a single detriment to moving to HFS launch from the LHCD physics point of view. Radial penetration, ray trajectories that avoid edge absorption, single pass absorption, accessibility, and overall current drive efficiency all improve with HFS launch. Fortuitously, if the balanced double-null (BDN) magnetic configuration is used, this design is also the most consistent with protecting the launching structures because the heat flux is much smaller on the inner, isolated SOL. From a physics point of view, it is clearly advantageous to launch the waves in regions of good curvature, since local filamentary structures, if any, then tend to propagate radially away from the launcher. Therefore, in our judgment, the inherent physics gains of HFS launch far outweigh the engineering demands, since these demands can be met if the HFS launch is integrated into the tokamak design from the onset.

[2]

[3]

[4]

[5] [6] [7] [8]

5.2. Future work [9]

While we focused on the steady-state portion of the discharge, there are still several questions that remain pertaining to the Vulcan auxiliary current drive system such as window locations, heat removal, and damaged launcher procedures. Perhaps most importantly, though, the method of plasma startup needs to be analyzed self-consistently. LHCD requires an already-hot plasma in order to function, so either a central solenoid or alternate auxiliary systems need to be used to initially attain the presently-analyzed plasma. It is possible to use higher n lower hybrid launch in order to assist with plasma startup, and then use the system described in this paper for steady-state operation. A system such as this would also allow for the development of time-dependent scenarios for evolving the plasma discharge. Given this work’s reliance on the benefits of HFS launch, experimental verification of these benefits would also be highly desirable. 6. Summary and conclusions An auxiliary current drive system for Vulcan has been conceptually designed. A variety of innovations were used in this design including high-field side launch of LH waves, integrated waveguides and splitters, and designated ports for the system. The high-field side launch design provides many physics and engineering advantages such as better launcher protection, better control over the damping location of the waves, and improved lower hybrid current drive efficiencies. Current-drive efficiency and plasma behavior was modeled using the ACCOME code, finding an optimized solution and confirming desirable plasma current profiles with q > 2 and bootstrap current fractions approaching 70%. This suggests that Vulcan can robustly operate non-inductive scenarios over a wide range of densities as required to fulfill its plasma-materials interaction mission.

[10]

[11] [12] [13]

[14]

[15] [16]

[17]

[18] [19]

[20]

[21] [22]

[23]

[24]

Acknowledgements The authors thank S.J. Wukitch for his valuable advice and G.M. Wallace for his consultations on the intricacies of LHCD systems. Y.A. Podpaly is supported by the Fusion Energy Sciences Program, administered by Oak Ridge Institute for Science and Education under a contract between the U.S. Department of Energy and the Oak Ridge Associated Universities. G.M. Olynyk is supported by the Natural Sciences & Engineering Research Council of Canada PGS D program.

[25]

[26]

[27]

[28] [29]

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