Prsentation PowerPoint

1
Non-linear MHD modelling of RMPs with toroidal
rotation and resonant and non-resonant plasma
braking.
M.Becoulet G. Huysmans, E. Nardon Association
Euratom-CEA, CEA Cadarache, F-13108, St.
Paul-lez-Durance, France. Thanks to all USBPO
RMPs team and especially to M. Schaffer and S.
Sabbagh

• Outline
• MHD model with resonant (jxB) and non-resonant
  (NTV) plasma braking.
• Example for 18 picture frame coils.

2
code RMHD reduced non-linear MHD A.Y Aydemir,
Phys.Fluids B4(11)1992,3469 in cylindrical
geometry, but with some new physics
included -Doppler shift due to the toroidal
rotation -resonant (jxB) braking Y.Kikuchi et
al PPCF 48(2006)169,E. Lazzaro et al
PoP9(2002)3906 -non-resonant braking K.
Shaing, PoP 10(2003)1443, W.Zhu et al
PRL96,225002(2006), due to the Neoclassical
Toroidal Viscosity (NTV).
Vorticity
Pressure (0 here)

Poloidal flux
Parallel velocity (Source is adapted
)
3
Calculation of Neoclassical Toroidal Viscosity
(NTV) in collisionless regime.(W.Zhu PRL2006)
-used here
4
Complete eliptic integrals of first (K) and
second (E) kind.
5
Example of the spectrum from 18 picture-frame
coils around ports in-vessel.
R1 8.608m Z11.798 R2 8.664 Z2-0. 558
df12.620 Dc-c20. PF-coil currents (A)
(nmax4) 19140. 110000. 19140. -103400.
-55000. 84260. 84260. -55000. -103400.
19140. 110000. 19140. -103400. -55000.
84260. 84260. -55000. -103400.
6
Chirikov parameter and normalized radial magnetic
field in cylindrical approximation for H-mode,
Hybrid and ITB q-profiles. For peak current
110kAt,n-4 edge (gt0.9) is ergodized.
7
Islands size in cylindrical approximation for
H-mode, Hybrid and ITB q-profiles.
8
Toroidal harmonic n-4 of poloidal plux
perturbation.
9
Input for RMHD code normalized ybnd at ra.
n-4
10
Equilibrium components needed for calculations of
NTV. ITER H-mode.
11
-magnetic field strength along non-perturbed line.
12
Poloidal harmonics for magnetic field strength.
Non-resonant m0 is the largestgt typical for
one-row coils.
13
Integral Il in the expression for NTV. Here only
n4 is taken into account. Possibly n14 will be
important. Non-resonant harmonics are more
important. Also they are not screened by
rotation, so one can take vacuum amplitudes for
these harmonics.
14
Plasma parameters (H-mode) for estimations of NTV
from 18pf coils (n4).
15
NTV force and damping time (0.4s on r0.4) for
ITER H-mode parameters with 18 picture-frame
coils at I110kA. Here only n4 is taken into
account. Possibly with n14 damping time will be
a bit shorter.
Damping time
NTV force
16
Non-linear MHD modelling with rotation and only
resonant braking. n-4, m1014
ybnd(2.5m102m111.5m12 1.25m131m14
)10-4 h(0)10-8 (here plasma resistivility is
higher compared to real one 10-9-10-10)
Resistivity profile
q-profile
17
Central islands are more screened, but edge
ergodisation persist smaller rotation, larger
resistivilygtless screening at the edge.
2p
Vt0 t8000tA
q
0
Vt0.5610-2 t8000tA, only resonant braking
r
1.
0.7
18
More external harmonics are less screened by
rotation. ymn q-m/n with (Vt0.0056) and without
rotation.
Resonant braking near q-m/n surfaces
6
19
How the most central (most screened) harmonics
n-4,m10 looks like (t8000tA)
20
Convective cells are formed in the ergodic zone
(seen also in JOREK code E. Nardon PoP
2007)gtdensity transport?
21
Initial rotation profile corresponds to
ft(0)1kHz (ITER-like). Resonant (jxB) braking is
localized near q-m/n surfaces. With NTV global
braking is observed. Here normal toroidal
viscosity m//10-6, NTV has a calculated form
(p.13) with maximum mNTV,max10-6 . Its a bit
higher (to see more rapid braking in modelling)
compared to our estimations 5.10-7 on p.13)
It is not stationary profile yet! Braking
continues.
22
Here similar weak screening for m10 with jxb
resonant braking and both jxB and NTV.
Vt0 t8000tA
jxBVt0.0056 t8000tA
jxBNTV Vt0.0056 t80000tA
23
More external harmonics are less screened by
rotationgt edge erdodisation. ymn q-m/n with
(Vt0.0056) and without rotation.
Total braking near q-m/n surfaces
24
Conclusions (from previous presentation)
-Penetration time increases like
1/resistivity. For ITERto the top of the
pedestal1s! -Larger amplitudes are less screened
by rotation. -Edge islands are much less screened
than ymnon q-m/n. -Edge is ergodised even with
strong rotation( DIII-D like). -ITER rotation
screens central (mlt8) non-resonant ,edge is
ergodised. -Non-resonant harmonics are not
screened by rotation. Conclusions (from this
presentation) -one row design (here 18
picture-frame coils, but its typical for one row
designs) give large amplitudes of non-resonant
harmonics in the plasma centre, notice also that
they are not screened by plasma rotation. -The
NTV calculated according to K. Shaing in
collisionless regime gives damping time 0.4s at
r0.4 (ITER H-mode,18pf coils, n4) -Edge
ergodisation here is weakly influenced by plasma
braking, since the initial rotation was already
weak. More external islands (here mgt10) are less
screened by rotation, since resistivity is larger
and rotation is slower. However , here we are
still two orders of magnitude larger resistivity
on the top of the pedestal, so screening is
expected to be larger. To be continued...