Vol.3, No.8, 738-742 (2011) Natural Science
http://dx.doi.org/10.4236/ns.2011.38098
Simulation of small size divertor tokamak plasma edge
under effect of toroidal magnetic field reversal
Amr H. Bekheit
Plasma & Nuclear Fusion department, Nuclear Research Centre, Atomic Energy Authority, Cairo, Egypt;
Received 3 February 2011; revised 26 March 2011; accepted 6 April 2011.
ABSTRACT
Asymmetries between the divertor legs of small
size divertor (SSD) tokamak plasma edge are
noticed to reverse when the direction of toroidal
magnetic field is reversed. In the present paper
the small size divertor tokamak plasma edge
under effect of toroidal magnetic field reversal
is simulated by B2SOLPS0.5.2D fluid transport
code. The simulation demonstrate the following
results: 1) Parallel (toroidal) flow flux and Mach
number up to 0.6 at higher plasma density re-
verse with reverse toroidal magnetic direction in
the edge plasma of small size divertor tokamak.
2) The radial electric field is toroidal magnetic
direction independence in edge plasma of small
size divertor tokamak. 3) For normal and reverse
toroidal magnetic field, the strong ITB is located
between the positions of the maximum and
minimum values of the radial electric field shear.
4) Simulation result shows that, the structure of
radial electric field at high field side (HFS) and
low field side (LFS) is different. This difference
result from the change in the parallel flux flows
in the scrape off layer (SOL) to plasma core
through separatrix. 5) At a region of strong ra-
dial electric field shear, a large reduction of
poloidal rotation was observed. 6) The poloidal
rotation is toroidal magnetic field direction de-
pendence.
Keywords: Reverse Toroidal Field;
B2SOLPS0.5.2D Code; ITB
1. INTRODUCTION
As a general trend, in single null divertor plasma, the
in-out asymmetries in power and particle profile have
long been observed between the divertor legs [1]. These
asymmetries disappear or change significantly when the
main toroidal magnetic field BT is reversed [2,3]. Rever-
sal the direction of the toroidal magnetic field has been
shown to alter these asymmetries and is accompanied by
changes in the amount and location of radiation [2]. Also
the direction of toroidal magnetic field determines the
direction of plasma particles drifts. Therefore, the
asymmetries that are sensitive to the field direction are
almost certainly a reflection of the drifts [2]. In the ex-
periment, in-out asymmetries show strong variance with
discharge parameters, and in particular with the direction
of toroidal magnetic field, BT reversal can help in estab-
lishing the physical mechanisms discriminate in their
effect on the asymmetries between ion and electron
drifts sides rather than between inner and outer sides [2].
The reversal of BT exchanges the sides, while the rever-
sal of IP (poloidal current) leaves than unchanged. In
this paper, we focus on the study of the of the reverse
toroidal magnetic field direction on the edge plasma of
small size divertor tokamak using 2-D SOLPS0.5 fluid
transport code [1,4]; including the calculation of the ra-
dial electric field Er. The basic item of “small size di-
vertor tokamak (SSDT)” is stainless-steel discharge ves-
sel consisting of two toroidal segments insulated from
each other and sealed off by an O-ring. The chamber has
rectangular cross-section 25 cm by 20 cm. Six large lat-
eral ports and 12 smaller windows at top and bottom of
the vessel allow a good optical access to the entire
plasma cross-section. The 180 toroidal field coils TF are
directly glued on the vessel by epoxy resin. This makes
dismantling and reconstruction of the tokamak very easy
(1 day). The computation region for simulation of small
size divertor tokamak is based on SN (Single Null)
magnetic divertor and covers the SOL (Scrip Off Layer),
core and private regions as shown in Figure 1. In com-
putation region the coordinate which vary in the direc-
tion along flux surfaces (x-coordinate or poloidal coor-
dinate) and the coordinate which vary in the direction
across flux surfaces (y-coordinate or radial coordinate).
The computation mesh is divided into 24 × 96 units
(where –1  x  96, –1  y  24 ) and the separatrix was

A. H. Bekheit / Natural Science 3 (2011) 738-742
739739
Figure 1. Coordinate system and simulation mesh: x is the
poloidal coordinate, y is the radial coordinate orthogonal to the
flux surfaces. The directions of magnetic field and plasma
current correspond to normal operation of conditions of SSD
tokamak (B drift of ions directed towards the x-point).
at y = 12. The simulations were performed for L-regimes
of SSDT (minor radius a = 0.1 m, major radius R = 0.3
m, I = 50kA, BT = 1.7 T, electron density at equatorial
mid-plane ne = ni = n = 4 × 1019 m–3, temperature heating
Ti = 6.9K eV).The small size divertor tokamak has a lot
of capabilities to study carefully cleaning and condition-
ing procedures. A fast and unproblematic exchange of
magnetic divertors with different materials is possible
and their influence on the plasma state can be examined.
Most of the diagnostic techniques valuable for investiga-
tion of large tokamaks are applicable on small size to-
kamaks. Careful measurements of averaged plasma
quantities may serve to improve the theoretical descrip-
tion of transport processes in the plasma bulk, in the
SOL, the wall and divertor plates. The small size diver-
tor (SSD) tokamak has a lot of application to study the
following subjects [5]:
1) Study of plasma–surface interaction processes.
2) Compatibility tests of divertor material and plasma.
3) Influence of wall conditioning (Carbonisation, bo-
ronisation, siliconisation etc)
4) Fluctuation measurements, in particular by probes
5) Study the transport processes in plasma (transport
theory )
6) Study spectroscopic analysis of impurities transport
in plasma
7) Study the physics of edge plasma
8) Study the transition from low to high confinement
(L-H) transition
9) Study the behavior of neutral particles near wall
and divertor plates
10) Study the Material testing
11) The SSD tokomak experiment provides the possi-
bility to study equilibrium, and the (resistive) MHD be-
havior of low-beta tokamak plasmas.
12) It will provide a very good opportunity in the fu-
ture for students and young scientists to become ac-
quainted with modern techniques the physics underlying
the fusion research.
The present paper demonstrated that, the radial elec-
tric field of small size divertor tokamak independent on
the toroidal magnetic field direction .The structure of the
radial electric field at higher field side (HFS) and low
field side (LFS) are discussed in this paper.
2. THE MAIN SIMULATION RESULTS
The B2.SOLPES0.5.2D code is used for present mod-
eling. The code employed to solve the full two dimen-
sional problem of the SOL multifluid transport Equa-
tions [4] uses an edge geometry and input assumptions
for plasma transport based on a comparison with ex-
perimental data from other tokamaks. Multifluid plasmas
consist of neutral particles, ions and electrons with vari-
ous physical processes (e.g. ionization, recombination
and charge exchange) [4].
The simulations were performed with B2SOLPS0.5.2D
fluid transport code. As in similar codes the set of modi-
fied Braginski equations was solved [1-4]. The philoso-
phy B2SOLPS0.5.2D fluid transport code (and other
codes) is that the values of perpendicular transport coef-
ficients are chosen to fit experimentally observed density,
temperature radial profiles, density and temperature near
the divertor plates. In the simulation presented below the
perpendicular transport coefficients are replaced by the
anomalous values: diffusion, electron, ion heat flux and
perpendicular viscosity coefficients [1-4]. The perpen-
dicular (anomalous) viscosity coefficient was taken in
the form  = n·mi·D. At the inner boundary flux surface,
which was located few cm from the separatrix, the den-
sity; the electron, ion heat fluxes and the average tor-
oidal momentum flux were specified [1-4]. The bound-
ary heat fluxes were imposed independently from the
toroidal momentum flux thus providing the opportunity
to investigate the dependence of radial electric field on
these parameters [1-4]. For small size divertor tokamak
operation, the simple anomalous cross-field transport is
characterized by a particle diffusivity D (AN) = 0.5 m2/s,
electron and ion heat diffusivities 
e, i = 0.7 m2/s. The
parallel heat and momentum transport are classical but
flux limited. The computational region for modeling is
based on SN (Single null) and covers the outer SOL and
the divertor below the midplane plus a small segment of

A. H. Bekheit / Natural Science 3 (2011) 738-742 740
the region of closed flux surfaces and the private flux
region(see Figure 1). The boundary conditions for mod-
eling are given (1-4). The case of unbalance neutral
beam injection is considered in this simulation. The
main results of simulation are:
1) Typical profile of the radial electric field and ion
temperature in both toroidal magnetic field directions
(normal and reverse toroidal magnetic field) are presents
in Figure 2, 3. In this case the radial electric field and
radial ion temperature distribution are almost independ-
ent of the direction of toroidal magnetic field BT.
2) Parallel (toroidal) flow flux is reverse with reverse
toroidal magnetic field direction, with Mach number
(
s
ii
M
VC, where Cs is sound speed) up to 0.6 in the
SOL as shown in Figures 4, 5. Figures 4, 5 shows also
the toroidal (parallel) flow flux is toroidal magnetic field
BT -dependence.
3) The structure of the radial electric at (HFS) and
Figure 2. The radial distribution of radial
electric field at normal and reverse toroidal
magnetic field.
0510 15 20 25
3.0
3.5
4.0
4.5
______ reverse BT _ _ _ _ normal BT
Separatrix
Ti ( K e V )
y ( cm )
Figure 3. The radial distribution of ion tem-
perature at normal and reverse toroidal mag-
netic field.
0510 15 20 25
-4000
-3500
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
------ (-BT)
____(+BT)
Separatrix
Vll ( K m / sec )
y ( cm )
Figure 4. The radial distribution of toroidal
(Parallel) velocity at normal and reverse tor-
oidal magnetic field BT.
0510 15 20 25
-6
-4
-2
0
2
4
6
8
------ (-BT)
____(+BT)
Separatrix
Mll
y ( cm )
Figure 5. The radial distribution of parallel
Mach number at normal and reverse toroidal
magnetic field BT.
(LFS) are shown in Figures 6, 7. In Figures 6, 7, near
separatrix, the radial electric at HFS and LFS are non-
monotonic Here mainly the radial transport of parallel
momentum driven by parallel viscosity balance the
anomalous radial transport of parallel momentum driven
by anomalous viscosity. The non-monotonic electric
field is responsible for spikes near separatrix at (HFS)
and (LFS). The magnitude of this spikes are dependent
on plasma electrostatic potential at (HFS) and (LFS).
Also the sign and magnitude of this spikes are controlled
by controlled the toroidal (parallel) fluxes at (HFS) and
(LFS), which transport to SOL and divertors plates
through separatrix. This result agrees with the result [9].
4) The simulation result shows that, for reverse tor-
oidal magnetic field, the strong ITB is located between
the positions of maximum and minimum radial electric
field shear as shown as in Figure 8. This result consistent

A. H. Bekheit / Natural Science 3 (2011) 738-742
741741
5 101520
-20
-10
0
10
20
30
Separatrix
Er ( K V / m )
y ( cm )
Figure 6. The radial electric field distribution
at (HFS) in edge plasma of SSDT.
5101520
-300
-200
-100
0
100
200
300
400
Separat rix
Er ( K V / m )
y ( cm )
Figure 7. The radial electric field distribution
at (LFS) in edge plasma of SSDT.
0510 15 20
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Separatrix
density
E, shear
y ( cm )
-2x105
-1x105
0
1x105
2x105
3x105
4x105
5x10
5
n,1019 ( m-3 )
min. shear
max. shear
Electric field shear ( s-1 )
Figure 8. The radial distribution of plasma
density and electric field shear at reverse tor-
oidal magnetic field.
with the result [10,11]. This result is interesting since
they might help explain for reversed toroidal magnetic
field the easier transition to H-regime and strong ITB
formation in edge plasma of small size divertor tokamak
5) The simulation results shows that, at region of
strong shear of radial electric field a large reduction of
poloidal rotation was observed as shown in Figure 9.
Figure 9 shows that, the poloidal flux in SOL is very
weak and poloidal flux to the targets is 0.3% of total ion
flux across separatrix for normal direction of toroidal
magnetic, but for reverse direction of toroidal magnetic
field the poloidal flux to the targets is 0.02% of total ion
flux across separatrix.
6) The fifth result of simulation shows that, the rever-
sal toroidal magnetic field make strong change in the
divertor properties leading to inner divertor plate receive
heat flux greater than outer divertor plate as shown in
Figure 10. This result consistent with results of [6-8].
7) The sixth result of simulation shows that, the pol-
oidal heat flux is toroidal magnetic field direction de-
pendence as shown as in Figure 10.
3. CONCLUSIONS
The simulation provides the following results:
1) Parallel (toroidal) flow flux is reverse with reverse
Figure 9. The radial distribution of poloidal
heat flux and electric field at normal and re-
verse toroidal magnetic field.
0 20406080100
-2
0
2
4
inner plate
outer plate
...... reverse B ____ normal B
q
ix ( M W / m )
X ( cm )
Figure 10. The poloidal distribution of pol-
oidal heat flux at normal and reverse toroidal
magnetic field.

A. H. Bekheit / Natural Science 3 (2011) 738-742 742
toroidal magnetic field, with Mach number up to 0.6.
2) The radial electric field of small size divertor to-
kamak (SSDT) is toroidal magnetic field independence.
3) The simulation result shows that, for reverse tor-
oidal magnetic field, the strong ITB is located between
the positions of maximum and minimum radial electric
field shear. This result is interesting since they might
help explain for reversed toroidal magnetic field the
easier transition to H-regime and strong ITB formation
in edge plasma of small size divertor tokamak.
4) Near separatrix the radial electric field at (HFS)
and (LFS) are non-monotonic. The non-monotonic
structure of radial electric field is connected with the
radial transport of parallel (toroidal) momentum driven
by parallel (toroidal) viscosity balances the anomalous
radial transport driven anomalous viscosity. Also the
non-monotonic structure of radial electric field is re-
sponsible for spikes formed near separatrix at HFS and
LFS. The peaks of those spikes are dependent upon the
plasma electrostatic potential between plasma and mate-
rial walls and divertors plates. Also the sign and magni-
tude of this spikes are controlled by controlled the tor-
oidal (parallel) fluxes at (HFS) and (LFS), which trans-
port to SOL and divertors plates through separatrix.
5) The difference between the structure of the radial
electric field at HFS and LFS refer to the change in par-
allel flux transport to SOL through separatrix. This result
consistent with the result [9].
6) In the region of strong shear of radial electric field,
a large reduction of poloidal rotation was observed and
poloidal flux to the targets is 0.3% of total ion flux
across separatrix for normal direction of toroidal mag-
netic, but for reverse direction of toroidal magnetic field
the poloidal flux to the targets is 0.02% of total ion flux
across separatrix.
7) The poloidal heat flux is toroidal magnetic field di-
rection dependence.
8) The reversal toroidal magnetic field make strong
changes in the divertor properties leading to inner diver-
tor plate receive power flux greater than outer divertor
plate. This result consistent with results of [6-8].
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