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SWIP. 托卡马克位形优化. 高庆弟. 核工业西南物理研究院 成都. 1. Plasma shaping. Elongation is beneficial to plasma confinement by increasing the current holding capacity . Triangularity is beneficial to supresion some MHD instabilities Quadrangle shaping showing evidence to modify ELMs (DIII-D).

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SWIP

托卡马克位形优化

高庆弟

核工业西南物理研究院 成都


1. Plasma shaping

  • Elongation is beneficial to plasma confinement by increasing the current holding capacity .

  • Triangularity is beneficial to supresion some MHD instabilities

  • Quadrangle shaping showing evidence to modify ELMs (DIII-D)


Identification of the plasma boundary

EFIT code developed in GA has been used widely in the would for the plasma shaping control


Determination of the plasma boundary for the single null divertor plasma in HL-2A

Reconstructed boundary at 320ms for 2898 shot. (+ and + denotes the filament and the centroid of plasma current respectively. X point position (Xr=1.552m, Xz=-0.451m), the position of strike point Zi=-0.780m (inner), Zo=-0.812m (outer), the plasma geometric center (Rg=1.652m, Zg=-0.069m), the plasma current centroid (Rc=1.664m, Zc=0.007m), plasma minor radius ap= 0.380m, elongation k=1.085)


Plasma shaping in HL-2A divertor plasma in HL-2A


(c) divertor plasma in HL-2A

(b)

(a)

Fig.2.1 Magnetic geometry of (a) a plasma with a nearly circular cross – section, (b) a plasma with the X point moving inward (D-shape, k95=1.08, 95=0.44), (c) a plasma with modest elongation (elongated D-shape, k95 = 1.21, 95 = 0.41).


The triangularity variation with respect to the flux coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center

Fig.2.2 Triangularity of the D-shaped plasma,  versus the flux surface for the cases of hollow current profile (full line) and peaked current profile (dotted line).


2. Optimization of the plasma current profile coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center

  • Control and optimization of the plasma current profile is a key point in enhancing the plasma performance. Although several tools have been identified to modify transport directly, the effect of the current profile on transport is large and remains an important transport control feature.

  • HL-2A has two different RF systems. The LH power is generated with 2 klystrons 0f 0.5MW each and radiated by a multi-junction (212) antenna. The EC power is generated by 4 gyrotrons with 0.5MW each. Directions of the radiated EC beams can be varied toroidally and poloidally by rotating the steerable mirrors.

  • A tangential neutral beam line will be installed this year, with power of PNB = 2.0MW, and beam energy Eb = 50keV, and It will be upgraded to PNB = 3.0 MW. Another beam line is expected.


Dispersion relation in the LH frequency domain coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center

  • Frequency domain

    wci << w <<wce

    f = w/2p ≈ 107 109 1011 Hz (l ~ 10 cm)

  • Dispersion relation (cold plasma limit)


Ray tracing for LH waves coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center

R0

  • Wave propagation equations in the optical geometry:

  • Rays are radially reflected at the caustics,

    defined by:

  •  propagation domains:

    n||0: injected value; q = rBtor/RBpol


3 Fokker-Planck analysis coordinate is dependent on the plasma current profile, but for both hollow and peaked current profiles it decreases rapidly at the plasma boundary region while moving towards the plasma center

Kinetic equation

An electron kinetic equation can be written as

The wave diffusion operator is the 1-D divergence of the RF induced flux:

where Dql is the quasi-linear diffusion coefficient, and here it signifies a sum over all waves in existence on a flux surface, with the appropriate powers and velocities. A simple sum is used, which means that we assume there are no interference effects.


We employ a 1-D collision operator as given by Valeo and Eder,

with the collisional diffusion and drag coefficient given by

In solving for fe we set , because the time for equilibration between RF power and the electron distribution is short compared with the time for plasma to evolve. Then the solution for fe is an integral in velocity space,


Control of the electron velocity distribution function Eder,

LH waves can drive a fast electron tail

Maxwellian

bulk

superthermal

tail


Fig.1.1 Waveforms of the plasma current I Eder,p, loop voltage Vp, the NBI power PNB, and the LH wave power PLH

Fig.1.2 Magnetic geometry of the discharge


Fig.1.3 (a) The temporal evolution of LH wave driven current profile, and (b) q profiles at different times for the sustained RS discharge


Fig.1.4 (a) Waveforms of the plasma currents I profile, and (b) q profiles at different times for the sustained RS dischargep, ILH, IBS, INB, and IOH and (b) their profiles at t=1.0s for the sustained RS discharge


Fig.1.5 The ion temperature T profile, and (b) q profiles at different times for the sustained RS dischargei (full line), and magnetic shear s (dotted line) versus x


Fig.1.6 Time traces of a quasi-stationary RS discharge: (a) LHCD efficiency, CD and non-inductive current fraction, (b) the H-factor, H98(y,2) and normalized beta, N, (c) the locations of the minimum q (full line) and the minimum i (dotted line), (d) the central plasma temperatures (Ti, Te).


  • The H-mode transport barrier is localized at the plasma edge;

  • The pressure of the H-mode pedestal increases strongly with triangularity due to the increase in the margin by which the edge pressure gradient exceeds the ideal ballooning mode limit;

  • Therefore, the rather high triangularity located at the plasma edge is favorable to enhancing the confinement.


  • RS discharge with double transport barrier edge;

  • The elongated D-shape plasma (98=0.43, k98=1.23) is used to model the RS discharge. The geometry of the boundary (98% flux surface of the diverted plasma) is specified as a general function of time. It evolves from circular to elongated D-shape during the current ramping-up phase and then keeping the same shaped boundary in the current flattop phase. The interior flux surfaces, which are computed by solving the Grad-Shafranov equation, are parameterized by the square root of the normalized toroidal flux.

  • The standard target plasma described above is used, but the electron density profile has a modest change with a more obvious edge pedestal.

  • The current profile is still controlled by LHCD.


The double transport barrier is indicated by two abrupt decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point, min 0.55, and near the plasma edge,  0.95, respectively. The elevated heat diffusivity between the two minima separates the two barriers.

Fig.2.3 Profiles of q and ion heat diffusivity, i (at t=1.0s) for the elongated D-shape plasma.

Fig.2.4 Profile of ion temperature and the ion temperature gradient, Ti (at t=1.0s).


In the DB discharge the plasma confinement is enhanced, and decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point, normalized beta, N and H-factor, H98(y,2) are higher than in the RS configuration with L-mode edge(see Fig.1.6)

Fig.2.5 Time traces of an RS discharge with double transport barrier: (a) normalized beta, N, (b) H-factor, H98(y,2), (c) locations of the double transport barrier (two dotted lines), and location of the shear reversal point (full line). The fainter lines indicate the results of the RS with L-mode edge.


Profile control by ECH+LHCD decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point,

Employing LHCD for large-scale q(r) control in a low-density plasma ofne =1.01019m-3 and Ip = 400kA, BT = 2.43T is considered. The target plasma is heated by EC of 0.48MW + 0.47MW lunched from 2 gyrotrons. By adjusting the polar lunch angle the EC power from 2 gyrotrons deposits around r = 0.2 and r = 0.3 respectively.

The q-profile has a little change in the ECH phase. To control the current profile, 0.5 MW LH power in the current drive mode (the multi-junction antenna phasing =90) is injected. As the LH wave deposition primarily governed by a nonlinearity between the LH power deposition profile and the electron temperature profile, the q-profile adjusts slowly, and the safety factor between r=0.0 and r=0.7 evolves gradually to the new quasi-steady values on the resistive time scale.

FIG. 8 Temporary evolution of q at various flux surfaces.


After the current profile is fully relaxed, the decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point, q values of r = 0.0-0.6 constrict to a narrow range of 1.0-1.3 (Fig. 6), and a q-profile with weak shear region extended to x=0.6 and qa=3.21 is established. It is sustained until LHCD is turned off. Though the q-profile in the weak shear region is not as flat as that in the discharge controlled by ECCD, the absolute value of the magnetic shear s[(dq/dr)(r/q)] is rather low.

  • The Te-profile does not show a change corresponding to the optimized current profile as is often the case with an electron-ITB developed.

  • But the electron temperature increases largely, and its normalized gradient R/LT (where 1/LT = Te/Te) becomes larger than the critical gradient value (R/LT <10) for temperature profile stiffness in the confinement region of r < 0.8, characteristic of the suppression of ETG and/or TEM driven turbulences. These characteristics of the plasma confinement are consistent with the hybrid discharge scenarios.

FIG. 9 (a) q-profiles, and (b) absolute value of magnetic shear versus r at various times, (c) Te-profiles at t=0.4s (Ohmic phase ),and t=1.3s, thin black line indicating electron heating power.


Fully non-inductive current drive decreases of the ion heat diffusivity, of which the two minima are located near the shear reversal point,

Current profile at t = 1.4s: total plasma current jp (full line), ohmic current joh (thin full line), LH driven current jlh (dotted line), and EC driven current jecr (dashed line).


  • Parameters of the Ohmic target plasma: , Ip= 220kA, and BT=2.0T, deuterium gas. First, the plasma is heated by NBI (t=0.5-1.8s, PNBI=0.5MW, E=20.0keV), then higher LH power (PLH = 1.5MW) is injected into the NBI heated plasma during t=1.0 -1.5s with  = 170.

FIG. 10. (a) Ti – profile, (b) Te – profile (fainter line indicates the location of LH wave deposition), (c) q – profile. the case of NBI heating only at t=0.9s; the case of the NBI+LH heating at t=1.2s

NBI加热建立的热离子先进托卡马克(AT)位形


FIG. 3.5 (a) Electron temperature profiles during LH heating at t=0.9s ( ), and before LH heating at t=0.65s ( ). The fainter thin line indi-cates the location of LH absorption; (b) Electron thermal conductivity profile at t=0.9s. (c)q-profile at t=0.9s .

For comparison, the above Ohmic plasma (Te>Ti) is heated by the sameLH wave scheme only to establish hot electron scenario.


  • Higher power electron Landau heating establishes operation scenario of preferentially dominant electron heating. Electron tempera-ture increases significantly. In contrast to the large increment of the electron temperature, the ion temperature only has a small change (dotted lines in Fig. 4).

  • In the hot ion plasma, not only the electron temperature has a large increment, but the ion temperature increases signifi-cantly (from Ti0 = 1.5keV to Ti0 ~ 2.6keV) as well (full lines).

Fig. 4 Temporal evolution of Ti0 (blue line), and Te0 (purple lines). Full lines indicate hot ion mode (NBI+LH heating), and dotted lines indicate hot electron mode (LH heating only)


FIG. 12. Temporal evolution of Ti(0), scenario of preferentially dominant electron heating. Electron tempera-ture increases significantly. In contrast to the large increment of the electron temperature, the ion temperature only has a small change (dotted lines in Fig. 4).

RS plasma;non-RS plasma

FIG. 13. Temporal evolution of Ei,

RS plasma; non-RS plasma

A comparison for the ion confinement is made between the RS and non-RS discharge: RS discharge - the LH wave is injected with slightly asymmetric spectrum ( = 170); non-RS discharge - the LH wave is injected with purely symmetric spectrum ( = 180), in this case the q-profile with negative shear could not be formed since the off-axis current driven by the LH wave is not sufficient.


The energy variation of the injected particles can be described with fairly accuracy by the following energy loss equation when

With W in eV, the rate of the beam energy loss is

=

If we consider beam particles of energy W which undergo complete therma-lization, then the average fraction of the total energy given up by the beam particles, which goes into the thermal ions of the plasma, is


  • As the electron temperature increasing due to LHH, the verage fraction of beam energy that goes into the thermal ions increases.

  • However, when the many physics effects in the NBI heating is taken into account, the picture is different: the NBI power that goes directly into the bulk ions and the power introduced by thermalization of the beam ions compose the ion heating power, and it is nearly unchanged.

Fig. 2 Average fraction of beam energy that goes into the thermal ions, F_ion, versus time, full line: Pbi/(Pbi+Pbe); dotted line: Fi


Fig. 3 (a) NBI heating power, and (b) NBI power losses versus time. Pbi is the NBI power that goes into ions, Pbe the NBI power that goes into electrons, Pbth the power from thermalization of the beam ions, Pcx the NBI power lost by charge-exchange, Pshin the NBI power shone through, Porb the orbit loss power of the beam ions, and Pie the power loss by electron-ion coupling inside the ion-ITB.


Plasma equilibrium in a tokamak with current hole versus time. P

Experimental results in JT-60U

Experimental results in JET


  • M. S. Chu’s work versus time. P

  • Revisited the theory of Greene,Johnson, and Weimer [Phys. Fluids, 14, 671 (1971)] and extend the theory to include equilibria with a central current hole.

  • This type of equilibrium consists of a central region with constant pressure and no poloidal magnetic field.

  • The equations that determine equilibria in the current hole are less singular than near the magnetic axis. All the physical quantities exist and are finite. In particular, these include the case of a current jump at the current hole boundary.

  • Isolated equilibria with negative current in thecentral region could exist. But equilibria with negative currents in general do not have neighboringequilibria and thus cannot have experimental realization,


The rotational transform, versus time. P

The flux renormalization equation,

The usual hoop force balance equation,

The ellipticity equation,


An versus time. Pn/m = 0/1 resistive kink mode become unstable when the negative current creates a zero in the poloidal field (e. i. q is infinitive).This instability removes the negative current in the center and flattens the central current profile to zero


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