Proceedings of ITC/ISHW2007

Reactor System Analysis and Pellet Injection Simulation in Helicaland Tokamak Reactors
Y. Higashiyama, K. Yamazaki, J. Garciaa, H. Arimoto, T. Shoji
Nagoya University, Furo-cho, Chikusaku, Nagoya 464-8603, JapanaUniversitat Polite `cnica de Catalunya (UPC), Barcelona, Spain

In the future fusion reactor, the plasma density peaking is important for the increase in the fusion power gainand for the achievement of confinement improvement mode. The density control and the internal transport barrier(ITB) formation due to the pellet injection has been simulated in tokamak and helical reactors using the toroidaltransport linkage code TOTAL. Firstly, the pellet injection simulation is carried out including the neutral gas
shielding model and the mass relocation model in the TOTAL code, and the effectiveness of the high field side(HFS) pellet injection is clarified. Secondly, the ITB simulation with the pellet injection is carried out with theconfinement improvement model based on the ExB shear effects, and it is found that the deep pellet penetration is
helpful for the ITB formation as well as the plasma core fuelling in the reversed shear tokamk reactor, but the deeppellet penetration is not effective in the helical reactor.
Keywords: Transport simulation, Internal transport barrier, Pellet injection, Tokamak reactor, Helical reactor

1. Intoduction
The total fusion reactor power strongly depends on
the radial profile of plasma temperature and density, andthe density control is important to optimize reactor
operation. To control plasma density and pressure
profiles, the pellet injection is considered as a prospective
technique. The pellet injection is used for the plasma core
fuelling, and it brings a peaked density profile, so that thefusion power gain is increased. In JET and other tokamak
experiments, it was shown that the density profile
modifications disagree with pellet ablation theory [1] thatassumes the pellet particles remain on the magnetic fieldlines where they are ionized [2]. The pellet penetration
depth measured by the pellet light emission agreed wellwith the pellet ablation theory. This suggested that a fast
outward major-radius drift may occur during the pellet
ablation and toroidal symmetrization processes. To test
this hypothesis the experiment of the high-field side(HFS) pellet injection has done in ASDEX-Upgrade, andit was shown that the fuelling efficiency and thepenetration depth of pellets are improved [3]. The similar
results are observed in DIII-D [4] and other tokamak
experiments, and the HFS pellet injection is expected to
be an effective technique of plasma core fuelling in future
tokamak reactors.
The transport simulation studies have been carriedout focusing on the ITB formation in tokamak and helicalplasmas. When the ITB is formed in the plasma, it brings
good confinement and rather peaked pressure profile, soy-higashiyama@ees.nagoya-u.ac.jp

that the operation scenarios with the ITB in tokamas are
expected as enhanced performance modes such as high pmode [5], reversed shear mode [6], and pellet enhanced
performance mode (PEP) [7,8]. In helical systems theITB model based on Bohm and GyroBohm-like transportwith ExB shear flow effects has already been comparedwith the LHD experimental ITB [9] and this model isinspired from the JET mixed-model [10]. This model isintroduced into the toroidal transport linkage TOTALcode [11, 12], and is applied to the 1-dimensional (1-D)
ITB formation simulation of both 3-D equilibrium helicaland 2-D equilibrium tokamk plasmas.
Both the pellet injection and the ITB formation have
big influence on the density profile and the fusion power
output, so that we consider about operation scenario with
ITB formation by pellet injection density control inhelical and tokamak reactor plasmas by using the TOTAL
code. Section 2 will describe the details of the transportmodels and the HFS pellet injection model included inthe TOTAL code, and simulation results will be shown insection 3. The conclusion will be given in section 4.

2. TOTAL code
2.1. Transport model description
The Bohm and GyroBohm mixed transport modelwith the ExB shear flow effect has already been
compared with the helical and tokamak experimental
ITBs [9, 10]. The most widely accepted explanation forthe ITB formation relies on the suppression of ITG

Proceedings of ITC/ISHW2007
turbulence due to ExB shear flow. The suppression of theturbulence might occur when the ExB flow shearing rate
ExB exceeds the ITG linear growth rate
ITG . Theshearing rate ExB is defined as [13,14]
RBB

20E B

020Err RB,(1)

whereandare the correlation lengths of theambient turbulence in the radial and toroidal direction,and , Er , B and B are the equilibrium electrostatic
potential, the radial electric field, the poloidal andtoroidal magnetic field, respectively. In tokamaks, theradial electric field Er is not easily measured directly, sothat Er can be calculated from the plasma radial force
balance equation under the assumption that the poloidal
velocities can be expressed according to the neoclassicaltheory [15, 16]. However in this paper, Er is described
simply asdEr
dr

1 dni dpi ,eni2 dr dr(2)in the H-mode condition [17], where ni and pi are ion
density and ion pressure, respectively. The ITG growthrate ITG is defined as [18]

2/3

i
ITG

where

1/ 2s ciqR,(3)

Ti / mi , and s is the magnetic

i = Ln/LT , ci =shear defined asr dq .
q drs(4)

Most theoretical studies based on the ExB shear
stabilization adopt a thermal diffusion coefficient
inthe forme, ineoclassicalanomalous

anomalous,Gyrobohm

1(5)
Bohm

2F

2.2. HFS pellet injection
The high-field-side (HFS) pellet injection isdescribed as two processes which are the pellet ablationand the mass relocation. We simulate the HFS injection
with the pellet penetration model combined with theablation model and the mass relocation model. There area few models which satisfactorily describe the pellet
ablation and give similar results [19]. So, we use here themost popular one: the neutral gas shielding (NGS) model[1]. The mass relocation width from ablation point withthe plasmoid drift in the major-radius direction R is
described as [20]R

0.5q Bt B p 1 1 qLe / aa 2 r02 n n

1.
n(8)

1

3. Simulation results
3.1. Demonstration of HFS pellet injection
The reactor machine parameters used in this paper
were those of typical designs optimized using the reactor
design system code PEC (Physics- Engineering- Cost)[12]. These parameters are derived from two 1GW
electric power fusion reactor designs; high-field high-betacompact tokamak reactor TR-1 (major radius R=5.2m,magnetic field B=7.1T) and high-beta helical system
HR-1 (R=12.1m, B=4.6T).
Typical results of the HFS pellet injection simulation
in tokamak reactor are shown in figure 1. The pellet
ablation densities are shown for the different pellet
injection velocity. Here, the radial parabolic temperatureand flat density profiles are assumed as T(x)=T0(1-x2)3,n(x)=n0(1-x2)0.5 with T0=30kev and <n>=1020m-3. This
figure shows that the HFS injection could provide rather
deep fuelling in the reactor-grade tokamak plasma, andthe further increase in the injection velocity improves thecentral fuelling. For assumed temperature and density, (6)

E B
ITG

whereF.

1E B
ITG(7)

2

1E B
ITG

The coefficient neoclassical is the neoclassical part ofthermal diffusion coefficient, and anomalous is theanomalous part described as the Bohm and GyroBohm
mixed transport model [9, 10]. And particle diffusion
coefficient D is assumed as D= e,i /Cano , in this paper
Cano=3 (tokamak) and 1 (helical).

Figure 1. Model prediction for the HFS pellet injection intokamak reactor. Ablation profiles are shown by a, b and c,and HFS injection simulation results are given by d, e, and fdepending on the pellet injection velocities. The profiles d ande are in the normal shear case, and f is in the reversed shearcase.

Proceedings of ITC/ISHW2007
profiles, the HFS injection with the pellet velocity of 1
km/s could provide the density increase at the normalizedradius r/a~0.1. Moreover, it shows that the reversed shear
mode improves the central fuelling for the HFS injection
based on the mass relocation model of equation (8).

3.2. ITB simulation with pellet injection
In the previous subsection, we show that the pellet
injection could provide deep fuelling in tokamak reactor
by the HFS injection. So that we consider about operation
scenario with ITB formation in deep (by HFS injection)and shallow (bymedium field side injection)
penetration depth cases in the reversed shear ITB
plasmas.
The figure 2 shows the operation scenarios of thetokamak reactor (reversed shear mode) in deep
penetration case by HFS pellet injection. Alpha particle
power and density are feedback-controlled by theadjustment of both heating power and fuelling. In thisscenario, ITB is formed at 15 sec and plasma is ignited at
100 sec. The figure 3 shows the comparisons with radialprofiles at steady state (time=200 sec) in deep (same asfigure 2) and shallow cases. We can see that there areclear differences between both cases. In the deep
penetration case shown in the left-hand of the figure 3,
the ITB is formed at ~0.4, but in the shallow case in theright-hand figure the ITB is not formed.
This reason is shown in the bottom two figures infigure 3. In this simulation, the ITB formation isdetermined by two parameters, ExB and ITG. In bothcases, ITG is reduced at ~0.4 where the magnetic shears~0. The suppression occurs when ExB exceeds ITG, sothe ITB tends to be formed at low ITG position. However,Figure 2. Figure (a) and (b) show the operation scenarios ofthe TR-1 (reversed shear) with HFS pellet injection. The
improvement factor F( ExB/ ITG) which is defined in theequation (7) is the value at =0.4. Figure (c) and (d) show
the time evolution of the electron density and temperatureradial profiles.

in the shallow penetration case the rate ExB is small at~0.4, because the gradient of radial electric field dEr/dris small depending on the term dni/dr in equation (2).
The transient density profile and the relevant clear ITB
formation depend on the pellet penetration depth. The
deeper pellet penetration brings the larger gradient of Er
and the larger shearing rate ExB at the position of small
ITG, so that the ITB is formed there. We can say that thedeep pellet penetration plays an important role in the ITB
formation, and the HFS pellet injection is a quite
effective technique for the confinement improvement aswell as the core density fuelling in the reversed shear
tokamak reactor.
Figure 4 shows the results of the ITB simulation in
the helical reactor. It is compared with deep and shallow
pellet penetration depth cases (same in tokamak). In thissimulation, different from tokamak case, the deep
penetration case corresponds to the high speed pellet
injection and not to the HFS injection, because theeffectiveness of HFS injection has not been observed sofar in helical system [21]. This might be because the field
connection length between the high filed side and the low
filed side is quite short in comparison with tokamak case.
In the helical reactor, the radial electric filed isdetermined from the ambipolarity condition of helicalripple-induced neoclassical flux, and the large gradient ofradial electric filed appears at the position of pellet
penetration ‘toe point’ (after this, we call this large
electric field gradient the ‘sharp valley’). The electricfield is influenced by the pellet penetration depth throughFigure 3. ITB simulation results with pellet injection in thereversed shear tokamak reactor. Left figures denote deeppellet penetration case (by HFS), and right figures are shallow
penetration case (by the medium field side injection). The
upper figures (a) and (c) show ion and electron temperatures,electron density, and pellet deposition profiles, and the lower
figures (b) and (d) show ExB and ITG profiles.

Proceedings of ITC/ISHW2007

References[1]

Parks P B and Turnbull R J 1978 Phys. Fluids 21 1735

[2]

Bayler L R et al 1992 Nucl. Fusion 32 2177

[3]

Lang P T et al 1997 Phys. Rev. Lett. 79 1478

[4]

Bayler L R et al 1998 Fusion Technol. 34 425[5]Ishida S et al 1993 Proc. 14th Int. Conf. Plasma Physics
Controlled Nuclear Fusion Research (W¨urzburg,1992)
vol 1 (Vienna: IAEA) p 219[6]

Kimura H et al 1996 Phys. Plasmas 3 1943

[7]

JET Team (presented by Schmidt G L) 1989 Proc. 12th
Int. Conf. Plasma Physics and Controlled NuclearFusion Research (Nice, 1988) vol 1 (Vienna: IAEA) p 215

Figure 4. ITB simulation results with pellet injection inhelical reactor. The left-hand figure corresponds to theshallow penetration case (pellet size = 4mm, injection
velocity = 1.0 km/s), and the right-hand figure is the deep
penetration case (pellet size = 6mm, injection velocity = 5.0km/s). The upper figures (a),(c) show radial electric field andpellet deposition profiles, and the lower figures (b),(d) shows
the improvement factor F( ExB/ ITG) which is defined in theequation (7).

the density profile, which is similar to the tokamak case.
But it is not same as in the tokamak that the ITB isformed in the both deep and shallow cases. The ‘sharpvalley’ can be formed at the ‘toe point’ of the pellet
penetration as shown in figure 4. In the deeper
penetration case the sharp valley tends to be smaller, andthe shearing rate ExB becomes smaller, therefore thereduction in the anomalous transport becomes weaker.
These results show that the deeper pellet penetration is
not needed for the ITB formation in the helical reactor.

4. Conclusion
We investigated the relationship between the ITB
formation and the pellet injection in tokamk and helical
reactors. The high field side (HFS) pellet injection in thetokamak reactor was analyzed and its effectiveness wasclarified. In the tokamak reactor with reversed shear
profile, it was shown that the pellet penetration depth
plays an important role in the ITB formation, and theHFS injection would be an effective technique for theconfinement improvement as well as the plasma core
fuelling. In the helical reactor, we showed that the deeppellet penetration is not needed for the ITB formation
because the position of ITB is determined by theambipolar radial electric field ‘sharp valley’ and thepellet penetration ‘toe point’, and the deeper penetration
does not help the strong reduction in anomalous plasmatransport.

[8]Tubbing B et al 1991 Nucl. Fusion 31 839[9]Garcia J, Yamazaki K, Dies J and Izquierdo J 2006 Phys.
Rev. Lett. 96 105007[10] Tala T et al 2001 Plasma Phys. Control. Fusion 43 507[11] Yamazaki K and Amano T 1992 Nucl. Fusion 32 633.
[12] Yamazaki K et al 2006 Fusion Engineering and Design 812743[13] Hahm T S and Burrell K H 1995 Phys. Plasmas 2 1648
[14] Zhou P, Horton W and Sugama H 1999 Phys. Plasmas 62503[15] Ernst D R et al 2000 Phys. Plasmas 7, 615[16] Kim Y B, Diamond P H and Groebner R J 1991 Phys.
Fluids B 3 2050
[17] Hinton F L and Staebler G M 1993 Phys. Fluids B 5 1281
[18] Esposito B et al 2003 Plasma Phys. Control. Fusion 45 933[19] Baylor L R et al 1997 Nucl. Fusion 37 445[20] Polevoi A R and Shimada M 2001 Plasma Phys. Control.
Fusion 431525[21] Sakamoto R et al 2002 Plasma Phys. Control. Fusion
26B, P-1.074