HT-7HT-7 上的上的 MHDMHD 行为及行为及动力学致稳的实验研究动力学致稳的实验研究

HT-7

自然科学基金项目 No. 19675041, No. 10275068

毛剑珊2003/5

• 研究动机与背景• 托卡马克磁流体不稳定性基本概念及分类• HT-7 上典型的 MHD 行为的实验观察及分类•新经典撕裂模（ NTM ）及 DIII-D 、 JET 、 ASDEX-

U 上有关的研究简介• DIII-D 上用 ECCD 完全抑制 NTM 实验简介• HT-7HT-7 上动力学致稳的实验研究上动力学致稳的实验研究

HT-7OUTLINEOUTLINE

获得稳态、高参数聚变等离子体（高）一直是聚变界追求的目标。输运垒（内部、边界、双垒）的形成是实现托卡马克等离子体高约束的重要途径， MHD 不稳定性制约了 limit.

托卡马克等离子体 MHD 稳定性是目前世界聚变研究热点和前沿性课题之一。 ( 最近有关的参考文献很多） HT-7 实验研究取得重大进展 . 高参数、长脉冲放电出现 MHD 不稳定性，从而导致破裂是目前困扰 HT-7向更高参数、更长脉冲冲击的主要障碍之一。 认识和抑制和控制撕裂模不稳定性是一个重要课题。

HT-7研究动机与背景

Magnetohydrodynamic (MHD) Instabilities宏观不稳定性 微观不稳定性

1. 米尔诺夫振荡 (Mirnov Oscillation) 磁场的周期性振荡

撕裂模不稳定性 (tearing modes instabilities)

2. 锯齿振荡 (Sawteeth Oscillation)

等离子体芯部 m =1 的不稳定3. 破裂不稳定性 (Disruption)破裂的特征是等离子体的热能和磁能在毫秒量级内迅速流失，等离子体快速熄灭。例如 JET ，他们统计了各种破裂起因并将其分类为 18种破裂。还有一些大、中型装置如 TFTR 、ASDEX-U 和 JT-60U 等，则着重研究了高密度破裂、高β破裂和低 q破裂，并对与破裂共生的 VDE 和 HaLo 电流进行了较深入系统地实验研究

HT-7托卡马克等离子体的磁流体行为托卡马克等离子体的磁流体行为

HT-7

Tearing Modes

The tearing instability in a tokamak is driven by the radial gradient of the equilibrium toroidal current density. The name derives from tearing and rejoining of magnetic field lines,which occur during the instability as a consequence of finite resistivity. (J.Wesson “TOKAMAK” 1997)

(a) flux surfaces of m 3 islands of full width w.

O-pt

X-pt

R

(b) flux surfaces of m 2 n islands of full width w.

rB~

R

q(ra) = m / n (m - 极向模数， n - 环向模数 )

当等离子体出现非线性撕裂模时 ,磁场拓扑发生变化 ,嵌套整齐的轴对称磁面被撕裂，磁力线重联形成磁岛

在 HT-7 真空室内安装了两套 Mirnov 探针阵列，分别在 A段和C 段，每套有 12 个切向探针和 12 个法向探针，固定在真空室半径为 34cm 的小圆截面上

A

B

MTI-MT8

top view

C

D

LHCD

在 HT-7 真空室内安装了两套 Mirnov 探针阵列，分别在 A段和 C段，每套有 12个切向探针和 12个法向探针。

rB~

rB~

rB~

pB~pB

~

MHDMHD 的观察的观察 HT-7

( from B.Shen)

MHD MHD 的模数： 的模数： m=2 f= 7 kHz (Shot 52586)m=2 f= 7 kHz (Shot 52586) from B.Shen

HT-7

托卡马克等离子体的磁流体行为托卡马克等离子体的磁流体行为

from G. S. Xu.

HT-7 Island Width CalculationHT-7 Island Width Calculation

m=2

2

4

qr

s

drdq

mB

qrbw

~ 1 - 2 cm

White, R.B., et al., Phys. Fluids 20 (1977) 800

RI

Brq

rr

)(0

2

)(

2

0)1(1 2

2

)(

q

qa

a

qq

)/1( 220 arjj

1)0(

)(

q

aq

For a large aspect-ratio circular plasmaFor a large aspect-ratio circular plasma (J.Y.Zhao)P. H. Rutherford, Physics of Fluids 16, 1903 (1973)

The generalized Rutherford equation describes the dynamics of the island width

0.0 0.2 0.4 0.6 0.8 1.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

q

r/a

83.0a/r3q ; 67.0a/r2qIp=130KA, It=3899A

HT-7

HT-7 HT-7 MHDMHD 行为行为

.

.

98 年前

1998 年

HT-7

HT-7 HT-7 运行区运行区

初始等离子体过快的建立， dI/dt,dne/dt 过大，引起 MHDShot No.52290 dIp/dt=66KA/16ms=4.1MA/s( 这样的炮很多）

HT-7

HT-7 HT-7 MHDMHD 行为行为

dI/dt, 过大

慢过快

no MHD

HT-7

MHD induced disruption with LHCD MHD induced disruption with LHCD in the Ne range 1.3~1.8in the Ne range 1.3~1.8

HT-7

在低阶有理面附近过陡的压力梯度HT-7

低模数 MHD 不断增长，导致内能的迅速损失，引起电流通道收缩，最终导致破裂

0.65 0.70 0.75 0.800.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

we(

KJ)

time

59017

W ~ - 30%

LHCD+IBW at high Ne (2e19m-3)放电一开始就有 MHD ，整个放电不稳定

高密度是保证聚变堆功率密度所必须的重要指标，但在高密度下，辐射损失过大（总辐射功率 Ne2 ) ，当总辐射功率接近总加热功率，使边界区迅速冷却，导致低模数 MHD 不断增长，并最终导致破裂。但不同装置上表现的模式各有差异，JET 主要是 2/1,3/2 模， D-III 主要是 3/2 模 ,TFTR 主要是 1/1 模，而 ASDEX-U上 2/1 模和 3/1 模均存在，并观测到强烈的 MARFE 效应。此类破裂在全面破裂中所占比例最大， JET达 25% HT-7 主要是 2/1 模

高密度欧姆放电 : 充气过快，引起密度、温度的快变化，引起 MHD 。平衡条件的快速变化，而控制位移的响应跟不上，引起等离子体向器壁靠近，加大了与器壁的相互作用。

Ne(0)=3.05.6 6.3

97 年 13748# 密度 5.0e13cm-3

高参数高约束运行

大电流、高参数高约束运行 典型炮号 No.53291 Ip~200 kA, Ne~3.96 ， LHW~463kW ； IBW~189kW qa=2.78 q=1 面向外移（ r from 10 to 13cm) ，

电流极限破裂，即总电流超过磁流体稳定极限时产生的破裂，进入磁流体扭曲模不稳定参数区。 MHD 使杂质流的突然增加导致电流通道的收缩。

2000 年 39714# IP=255.2KAqa=2.26

初始位移快变引起初始位移快变引起 MHD MHD （硼化后）（硼化后）HT-7

No.52586 No.52586 全波驱动实验全波驱动实验放电后期放电后期 MHDMHD 引发破裂引发破裂 HT-7

长脉冲放电的后期，高温等离子体与限制器和真空室器长脉冲放电的后期，高温等离子体与限制器和真空室器壁长时间作用，引起杂质辐射壁长时间作用，引起杂质辐射 ,, 引起引起 MHDMHD ，导至破裂，导至破裂

HT-7

• A crucial issue for the extension of advanced tokamak scenarios to long pulse operation is to avoid these MHD instabilities.

• In configurations with transport barriers the improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density which often drive magnetohydrodynamic (MHD) instabilities neoclassical tearing mode (NTM) ， terminating the discharge or reducing the discharge performance. The edge and the core transport barriers deteriorate or are completely lost.

Neoclassical Tearing Mode (NTM)HT-7

* S. Günter, et al. “ Neoclassical tearing modes on ASDEX Upgrade: improved scaling laws, high confinement at high N and new stabilization experiments” NF/2003/Vol.43/No.3 161 (2003.3.10)

* S. Saarelma, et al , “MHD stability analysis of type II ELMs in ASDEX Upgrade” NF/2003/Vol.43/No.3 262

* M.F.F. Nave, et al. “Triggering of neo-classical tearing modes by mode coupling” NF/2003/Vol.43/No.3 179

* R.J. Buttery, et al “Onset of neoclassical tearing modes on JET” NF/2003/Vol.43/No.3 69

* A. Gude, et al, “Temporal evolution of neoclassical tearing modes and its effect on confinement reduction in ASDEX Upgrade” NF/2003/Vol.43/No.3 833

* F. Salzedas, et al “The effect of ECRH on the stability of the radiation induced m = 2 mode and on the current quench of a major disruption” NF/2003/Vol.43/No.3 881

The papers about neoclassical tearing mode (NTM)

)/(2/1'

2 pqR LL

dt

dW

r

J || bs 1/2 p / B

Lq ≡q / (dq / dr) 0 Lp ≡p / (dp / dr) 0

HT-7

The growth (or decay) of tearing mode islands is given by the Rutherford equation modified for the perturbed neoclassical bootstrap current[General Atomics Report GA–A23156]

is the poloidal beta, i.e., the plasma pressure relative to poloidal magnetic field pressure B

220

22.1/20rR local resistive diffusion time for local plasma resistivity

HT-7

No.52586 Ip~120 kA, Ne:1.2e19m-3 NH89 ~ 2 LHW~465kW ； IBW~220kW高参数，高约束运行状态下，放电后期 M=2锁模引起破裂

高参数高约束运行下，放电后期 M=2锁模引起破裂 典型炮号 No.52586 Ip~120 kA, Ne:1.2e19m-3 LHW~465kW ； IBW~220kW NH89 ~ 2

MHD developing sequencem=2 (7KHZ) was stimulated at 600ms, m=3 (15KHZ) at 650ms, mode locked at 750ms, major disruption at 770ms

No.59017 Ip=125KA Ne=2.4 X 1013cm-3 Bt (3768A) LHW=290KW IBW=200KW SX with lager sawteeth, no impurity increacing before MHD

Examples of q = 1 Sawteeth Inducing m/n = 3/2 NTMsfor DIII-D

Examples of q = 1 Sawteeth Inducing m/n = 3/2 NTMsThis mode can cause beta (at fixed input power) to drop by 10% ~ 30%.

Examples of q = 1 Sawteeth Inducing m/n = 3/2 NTMsfor JET

No.59017 Ip=125KA Ne=1.4 X 1013cm-3 Bt 1.75T(3768A) LHW=290KW IBW=200KW

A large MHD ( m=2) induced major disruption

SX with lager shouteeth, no impurity increacing before MHDA large q 1 sawtooth instability can produce a perturbation at q 2The presence of a “seed” island[J.L. Luxon, et al., Plasma Phys. and Control. FusionResearch, Vol. 1 (1987) p. 159]

0.65 0.70 0.75 0.800.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

we

(KJ)

time

59017

W ~ - 30%

0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

we

(KJ)

time

59017

LHCDIBW

No.53182 Ip=250KA Ne=1.6 X 1013cm-3 Bt ~1.97T(4229A) LHW=500KW IBW=250KW

No MHD on HT-7 high performance

Bt~1.8T, H89*N >3 (4) and H93>1 (1.5) for ~50E

HT-7

HT-7HT-7 可能引发可能引发 MHDMHD 的几种主要原因的几种主要原因• 初始等离子体过快的建立， dI/dt,dne/dt 过大，引起 MHD ( 解决办法：如， 400ms前程序控制， 400ms后投入加热场反馈 , 低环压起动，调节充气速率等）

• 长脉冲放电的后期，高温等离子体与限制器和真空室器壁长时间作用，引起杂质辐射 ( 解决办法：如注意水平位移的调节、水冷石墨限制器等）

• 高参数，高约束运行状态下，在某一局部形成过陡的压力梯度，特别是在低阶有理面附近过陡的压力梯度 NTM （避免办法：如改变 Ne,Bt,IBW 共振层， ECCD ，动力学致稳动力学致稳等 )

• 运行在极限条件下，如：高密度极限，大电流、低 q放电等等

• 。。。。。。

parallel heat flow along field lines dominates over cross-field transport and flattens the pressure in the island

“missing” bootstrapcurrent in O-point

MHD Instabilities Occurring near/atthe Transport Barrier on D-III Tokamak HT-7

The improved edge and core confinement leads to large pressure gradient and large edge bootstrap current density JBS (trapped particles and pressure gradient p )which often drive MHD to limit performance at higher poloidal beta

GA- A23843 & GA- 23255

**The development of techniques for neoclassical tearing mode (NTM) suppression or avoidance is crucial for successful high beta/high confinement tokamaks. **Localized off-axis co-current drive ECCD could replace the “missing” bootstrap current in the island O-point and stabilize the NTM [Phys. Plasmas 4, 2940 (1997)] *This(DIII-D) was confirmed both in ASDEX- U [Phys. Rev. Lett. 85, 1242 (2000)], and in JT-60U[Plasmas Phys. Control. Fusion 42, L37 (2001)] with electron cyclotron current drive (ECCD).

HT-7

ECCD SEARCH AND SUPPRESSION OF NTM

Ip~1.0-1.2MA, Bt=-1.52 to -1.64 T.The injected rf power Pec is up to 2.3 MW for four gyrotrons. The second harmonic resonance 2 fce for the 110 GHz gyrotron frequency Real-time control of optimum position for shot-to-shot and time-to-time variation in the optimum position with the plasma control system(PCS), PCS makes small changes in toroidal field BT

Best results (i.e. complete 3/2 NTM suppression) N increases by about 25% as the 3/2 NTM is suppressed and remains at this level even after the ECCD is turned off

For fixed Rsurf , the PCS can do a BT “blind search”. Here the step size is BT 0 .01 T, equivalent to R = 0.9 cm (B T/ B T ~0.6 %)

The q 3/ 2 location is essentially unchanged.

Searches and optimum until the optimum BT is adjusted and complete suppression NTM obtained

rB~

R

Modulate ECCD for suppression MHD on DIII-D

O-pt

X-pt

R

Large (w/ r~20% full width) m/ n3 2 neoclassical tearing modes in the presence of sawteeth are completely suppressed by precisely located (to 1cm) off-axis electron cyclotron current drive. A level of peak jec of about twice jbs is required for stabilization. A little higher value may be necessary if there is direct coupling of q 1 and q 3 /2 surfaces. The DIII-D plasma control system (PCS) has been developed to do real-time search and suppress position control using either rigid radial plasma shifts or adjustment of the toroidal field and thus second harmonic electron cyclotron resonance location. This represents the first use of active feedback control to position the ECCD.After NTM suppression with continued ECCD, beta could be substantially raised above the onset level. N increases by about 25% Future work is to apply ECCD to inhibit the onset of NTMs and will require the PCS to locate the q 3/ 2 surface, for example, and position the ECCD in the absence of the NTM, particularly as beta is increased and a Shafranov shift occurs. Future work will also be to suppress the m/ n2 /1 NTM.

ECCD NTM CONTROL

Dynamic Stabilization on the HT-7 Dynamic Stabilization on the HT-7 Superconducting TokamakSuperconducting Tokamak

Jianshan MaoSupport by National Natural

Science Fund of China No. 19675041 & 10275068

ASIPPASIPP HT-7HT-7