Plasma and Fusion Research: Regular Articles

Volume 11, 2403068 (2016)

Investigation of Ideal-MHD Stable Scenario for Plasma Current
Ramp-Up with No Magnetic Flux Consumption in JT-60SA∗)
Takuma WAKATSUKI, Takahiro SUZUKI, Nobuhiko HAYASHI,
Junya SHIRAISHI, Shunsuke IDE, Hirotaka KUBO and Yuichi TAKASE1)
Japan Atomic Energy Agency, Naka 311-0193, Japan
1)
University of Tokyo, Kashiwa 277-8561, Japan(Received 27 November 2015 / Accepted 18 March 2016)
Feasibility of plasma current ramp-up in JT-60SA with no additional central solenoid (CS) flux consumption
after the initial plasma formation has been investigated using an integrated modeling code suite (TOPICS). In
our previous study, we developed a scenario in which the plasma current is ramped-up from 0.6 MA to 2.1 MAwith no additional CS flux consumption by overdriving the plasma current using neutral beams (NB) and electron
cyclotron (EC) waves. While the density profiles were prescribed in the previous study, in this study, we introduce
a particle transport model according to the experimental results of JT-60U. It is shown that an internal transportbarrier (ITB) can be obtained and the plasma current can be overdriven even if the particle transport is solved.
The plasma current is ramped up in 330 s without CS flux consumption using 17 MW of NB and 3 MW of EC
when the electron density is approximately 70% of the Greenwald limit. Although low-n ideal MHD modes arestable, an infinite-n ballooning mode is unstable in this scenario. The latter mode is presumably harmless, but toensure the stability we investigate the pressure and the current profile controllability when the plasma current isoverdriven. As a result, the infinite-n ballooning mode is shown to be stable when a broad pressure profile and alocally optimized magnetic shear are obtained using 2 MW of on-axis N-NB, 2 MW of oﬀ-axis N-NB, 4 MW of
co-tangential P-NB and 7MW of EC with the electron density 30% of the Greenwald limit.
c 2016 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: plasma current overdrive, non-inductive, MHD stability, TOPICS, MARG2D, JT-60SA, simulation
DOI: 10.1585/pfr.11.2403068

1. Introduction
If the amount of magnetic flux swing capability ofcentral solenoid (CS) required for plasma current rampup is reduced, a strong constraint on the tokamak reactor designs is relaxed. Current start-up and/or rampup operations without CS flux consumption were demonstrated in many tokamaks, e.g. JT-60U [1], PLT [2], DIII-D[3]. Nonetheless, the experimental data on large tokamaks
which can confine reactor relevant high pressure plasmas
are not suﬃcient to ensure the extrapolability to the reactor
plasma.
We have investigated reduction of the CS flux requiredin the current ramp-up phase in JT-60SA using an integrated modeling code, TOPICS suite [4]. In the previous study on current ramp-up with reduced CS flux consumption in JT-60SA, we developed a scenario in which
the plasma current is ramped-up from 0.6 MA to 2.1 MA
in 150 s without additional CS flux consumption by overdriving the plasma current using neutral beams (NB) andelectron cyclotron (EC) waves [5]. Here, the plasma current overdrive means that the non-inductive current, which
is a sum of a bootstrap current, NB driven current and EC
author’s e-mail: wakatsuki.takuma@qst.go.jp∗) This article is based on the presentation at the 25th International Toki
Conference (ITC25).

driven current, exceeds the plasma current. The prescribed
density profiles which had strong internal transport barrier(ITB) and H-mode pedestal were used in previous study,
however, the pressure profiles were strongly dependent onthese prescribed density profiles. If the particle transport issolved, the width and the location of the density ITB might
be diﬀerent from the prescribed density profiles. Therefore, in this study we investigate the possibility of modification of the pressure profiles using the heating and current
drive (H & CD) actuators in JT-60SA by solving both theparticle transport and the thermal transport. In particular,
if local pressure gradient becomes too steep, a localized
mode such as an infinite-n ballooning mode might be unstable. In fact, the infinite-n ballooning mode is unstablein the previous study. Therefore, we investigate pressure
profile controllability in order to avoid infinite-n ballooning mode stability limit in addition to low-n mode stability which can be studied by an ideal MHD stability code
MARG2D.
This article is organized as follows. In section 2, characteristics of the modeling tools and the heating current
drive configurations of JT-60SA are described. An introduced particle transport model is also described in this section. The example of the current ramp-up scenario with no2403068-1

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CS flux consumption which is calculated according to theparticle and heating transport model is described in section
3. Controllability of pressure profile under the condition
that the plasma current is overdriven is shown in section 4,
and conclusions are given in section 5.

2. Modeling Tools and Assumed Experimental Conditions
TOPICS is an integrated modeling code suite and its
main part solves the 1-D transport equations [6] in accordance with the 2-D free boundary equilibrium. Several
turbulent models can be used for the integration of theanomalous heat transport in TOPICS. Among them, we use
CDBM model which demonstrated its ability to reproduce
plasma profiles with ITB in JT-60U [7, 8]. As for the particle transport calculation, we assume that the anomalous
particle diﬀusivity is proportional to the thermal diﬀusivity according to experimental results of JT-60U. In the reversed shear plasmas on JT-60U, the eﬀective particle diffusivity in the ITB region was estimated to be 0.04-0.2
times the ion thermal diﬀusivity when only the diﬀusion
term was considered [9]. Thus, we assume an eﬀective
anomalous particle diﬀusivity Dano = 0.2 × χCDBM,i andcalculate the particle transport assuming that the particle
diﬀusivity is a sum of neoclassical and anomalous diﬀusiv-

Fig. 1 NB trajectories and EC ray trajectories with a plasma
equilibrium. The NB trajectories of on-axis N-NB, oﬀaxis N-NB, co-tangential P-NB and perpendicular P-NB
are shown. The locations of the stabilizing plate, the vacuum vessel, the TF coil are also shown. EC ray trajectories with poloidal angles −20◦ , 0◦ and +20◦ are shown.

ities with zero anomalous particle pinch velocity. The neoclassical diﬀusivity is needed for including a strong neoclassical diﬀusion inside the reversed shear region. Particle
sources are NBI and the edge gas puﬀ. The volume averaged density is feedback controlled by the edge gas puﬀ.
JT-60SA will be equipped with two tangential negative ion based neutral beams (N-NB), 24 positive ion based
neutral beams (P-NB) and a steerable EC wave launcher asshown in Fig. 1. The beam energy of the N-NB will be
500 keV while that of the P-NB will be 85 keV. One of the
N-NB will be injected on-axis and the other will be oﬀaxis to the plasma magnetic axis, which can be used tomodify the current profile, and each beam power will be
5 MW. There will be three groups in the P-NB, which will
be co-tangential beams, counter-tangential beams and perpendicular beams to the plasma current. Co- and countertangential beams consist of four beams with 1 MW power
each, respectively, and perpendicular beams consist 16
beams with 1 MW power each. The maximum power ofthe EC wave will be 7 MW.

3. Plasma Current Overdrive
Figure 2 is one of the results of the ramp-up scenario
simulation. It is shown that the plasma current can be overdriven using the H & CD system of JT-60SA during theplasma current ramp-up even in the simulation in which
particle transport is solved. The plasma current is ramped
up from 0.6 MA to 2.1 MA without a flux consumption of
CS and equilibrium field (EF) coils. It takes 330 s (from5 s to 335 s) for the current ramp-up in this scenario. Thisduration is longer than the discharge duration of JT-60SA(100 s) and the duration in the previous study (150 s) [5],however, if more NB power is injected to shorten the rampup duration, the location of ITB moves outwards in minor radius and the confinement quality becomes too good.
Then, plasma beta becomes too high and the plasma becomes unstable.
At the low current (0.6 MA) phase, only co-tangential
P-NB and EC can be used because shine through lossesof on- and oﬀ-axis N-NBs and perpendicular P-NB arelarge. Therefore, the plasma current is overdriven using
co-tangential P-NB and EC from 5 s. The toroidal injection angle of EC wave is 10 degrees in the co-direction and
EC is locally absorbed around ρ = 0.45. On the other hand,once the plasma current exceeds 1 MA and the electron
density becomes higher than 1 × 1019 m−3 , shine throughlosses of on- and oﬀ-axis N-NBs and perpendicular P-NB
become less than 10%. In this scenario, we try not to use
EC in the high current phase because a localized EC current drive might be required for other purpose such as astabilization of neoclassical tearing modes.
Time evolution of the density profile, the temperature
profile and the safety factor profile are shown in Fig. 3.
The density and the temperature profiles at the edge region (ρ ≥ 0.85) is prescribed in order to assume appropri-

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Fig. 2 TOPICS simulation of a current ramp-up scenario from
0.6 MA to 2.1 MA without CS flux consumption. Timeevolution of (a) the plasma current (Ip ), non-inductive
current (INI ) and its three components, (b) CS and EF flux
consumption and its inductive and resistive component,(c) input powers used for the auxiliary heating and current drive, (d) the fraction of the electron density to theGreenwald density limit ( fGW ) and the gas puﬀ rate.

ate pedestal pressure height and width in accordance withthe scaling law by Cordey et al [10] and EPED-width scaling [11], respectively. We assume that the L-H transition takes place around 5 s because the threshold poweris 1.6 MW. The current driven by NB and EC and the bootstrap current consists a large oﬀ-axis current. Then, the reversed shear configuration which has the minimum valueof a safety factor (q) at an oﬀ-axis location is formed asshown in Fig. 3 (c). As a result, the ITBs in the density
and the temperature are formed as shown in Fig. 3 (a,b) because the anomalous transport is reduced at the region of
the weak or negative magnetic shear in CDBM model.
Nonetheless, the strength of ITB in the density is
weaker than the prescribed profiles used previously as
shown in Fig. 4 (a). This is because the particle source
by NB which can provide ions in the plasma core regionis small as shown in Fig. 4 (b). As a result, the bootstrap
current decreases compared with the previous case. Then,the electron density is kept lower in this scenario because
it was shown that the non-inductive current increases as

Fig. 3 Time evolutions of (a) the density profile, (b) the electron temperature profile and (c) the safety factor q in the
scenario shown in Fig. 2.

the electron density decreases. The fraction of the electron density to the Greenwald density limit ( fGW ) is kept
approximately 0.6 - 0.7 throughout the current ramp-up. If
we consider a pellet injection, stronger density ITB might
be attained, however, ideal MHD modes are thought tobe unstable when ITB becomes stronger as shown later.
Therefore we don’t consider a pellet injection in this study.
The stabilities of low-n (n = 1 - 3) ideal MHD modes
are investigated using a linear ideal MHD stability code
MARG2D [12]. These modes are stable if we assume
a perfectly conducting wall is placed at the location ofa vacuum vessel and a stabilizing plate of JT-60SA. On
the other hand, a normalized pressure gradient α =−(2μ0 Rq2 /B2 ) dp/dr is larger than the stability limit of an
infinite-n ballooning mode αcrit which can be calculated
from the ballooning equation [13] at 335 s as shown in
Fig. 5. A localized infinite-n ballooning mode might notcause a plasma disruption, however, can lead to a degradation of ITB. In addition, a localized mode near ITB whichcauses a minor collapse might be excited when the local

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Fig. 4 (a) Comparison of the calculated density profile and theprescribed density profile used in previous study [5] atthe current flat top. (b) Profiles of ion sources by the gas
puﬀ and NBI. Note that NBI particle source shown hereis magnified by 10 times.

Fig. 5 Profiles of the total plasma pressure (black, solid) and
α/αcrit (red, broken) at 335 s in the scenario shown in
Fig. 2.

pressure gradient is near the stability limit of infinite-n ballooning mode [14]. Therefore, we try to modify the pressure profile in order to avoid the infinite-n ballooning instability.

4. Pressure Profile Control
In order to investigate the pressure profile controllability under the condition that the plasma current shouldbe overdriven, we calculate many plasma current ramp-up
scenarios with diﬀerent H & CD inputs and electron densities. In these cases, durations of the plasma current rampup is reduced to 25 s in order to reduce computational cost.
Although the CS flux is consumed in this faster ramp-up
case, if the plasma current is shown to be overdriven in thiscalculation, CS-less current ramp-up becomes possible at
suﬃciently slow ramp-up rate using the same H & CD in-

Fig. 6 Profiles of (a) the total plasma pressure (solid) and thefast ion pressure (broken), (b) the normalized pressure
gradient α, (c) the ratio of α over αcrit and (d) the safety
factor q (solid) and the magnetic shear (broken) at 5 s and
Ip = 0.6 MA. Pink and Green lines represent the cases
3.02 MW of co-tangential P-NB and 7.00 MW of EC are
injected, respectively.

put. As for the representative time step, pressure profiles atthe beginning (5 s) and the end (30 s) of the plasma current
ramp-up is mainly investigated.
As is mentioned in the previous section, only tangential P-NB and EC can be used at the low current (0.6MA) phase before the plasma current ramp-up. Figure 6
shows diﬀerences in the profile of pressure, α, α/αcrit , q
and a magnetic shear (s = (ρ/q)dq/dρ) when 3.02 MWof co-tangential P-NB or 7.00 MW of EC are injected tothe plasma with the electron density which is approximately 60% of the Greenwald limit. While the P-NB input power (3.02 MW) was lower than a half of the EC
input power (7.00 MW), the non-inductive current drivenby P-NB (0.64 MA) was almost the same as that by EC(0.67 MA) because co-tangential P-NB has higher current
drive eﬃciencies than EC. When 3.02 MW of co-tangential
P-NB is applied, even though the pressure becomes higher
and α becomes larger in a wide region due to a large fast
ion pressure, α/αcrit is less than unity all over the plasma.
However, if 4 MW of co-tangential P-NB is injected, theballooning stability criterion is violated. Therefore, cotangential P-NB can overdrive the plasma current more efficiently than EC, but the input power should be kept suf-

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ficiently low in order to prevent the infinite-n ballooning
mode from being unstable.
On the other hand, α becomes large at a localized region when 7 MW of EC is applied. Although α of theEC case is larger than that of the P-NB case at this narrow region, α/αcrit is smaller. This is because the magnetic
shear becomes negative at this region due to the localized
current drive by EC. An infinite-n ballooning mode is stabilized when shear becomes small or negative, therefore,
αcrit becomes large. As a result, the plasma current is overdriven without violating the ballooning stability criterionusing 7 MW of EC. However, 7 MW is the upper limit ofavailable EC power of JT-60SA. Therefore, if plasma density is increased to 100% of the Greenwald limit, the current drive eﬃciency decreases and plasma current cannot
be overdriven by EC.
At the high current (2.1 MA at 30 s) phase, on- andoﬀ-axis N-NBs can be used for the current drive in addition to co-tangential P-NB. In Fig. 7 (a), the non-inductive
currents driven by co-tangential P-NB, on-axis N-NB oroﬀ-axis N-NB are compared with two densities which are
the same volume averaged density as the cases in Sec. 3( fGW ∼ 0.6) and half density of it ( fGW ∼ 0.3). In general,more non-inductive currents can be driven at low densities
and on- and oﬀ-axis N-NBs can drive the non-inductive
current more eﬃciently than co-tangential P-NB as alreadydiscussed in the previous paper. Figure 7 (b) shows thedependence of max(α/αcrit ) on the non-inductive current.
In general, max(α/αcrit ) increases as the density decreases
with the same input power because the slowing down timeof fast ions becomes longer and the fast ion pressure increases as shown in Fig. 7 (c).
However max(α/αcrit ) is not much depend on the density if we compare max(α/αcrit ) in cases that the almost
same non-inductive current is driven by a specific H & CD
source as shown in Fig. 7 (b). This is because almost thesame fast ion populations are needed to obtain the same
non-inductive currents. On the other hand, max(α/αcrit )can be decreased by using co-tangential P-NB rather than
N-NBs. Therefore, it is better to use co-tangential PNB preferentially. However, an available power of cotangential P-NB is limited to 4 MW. Lower density operations are preferable because a larger non-inductive current
can be driven by 4 MW of co-tangential P-NB and required
additional powers of N-NBs for the plasma current overdrive can be reduced.
In Fig. 8, the pressure profiles are compared when theplasma current is slightly overdriven by 6.42 MW of onaxis N-NB, 7.11 MW of oﬀ-axis N-NB or 11.04 MW of
co-tangential P-NB with the volume averaged density halfof the case in Sec. 3. In all the cases, the non-inductive
current is kept almost same (the diﬀerence is less than5%). Infinite-n ballooning modes become unstable at the
tail of fast ion profiles in on- and oﬀ-axis N-NB cases. On
the other hand, pressure gradient becomes less steep withco-tangential P-NB and α/αcrit becomes less than unity.

Fig. 7 Dependences of (a) the non-inductive driven current
on input powers, (b) max(α/αcrit ) on the non-inductive
driven current and (c) volume averaged pressure on input
powers. Closed and open symbols stand for cases withthe densities which are the same volume averaged density
as the cases in Sec. 3 ( fGW ∼ 0.6) and the half density ofit ( fGW ∼ 0.3), respectively. Circles, triangles and squares
represent the cases on-axis N-NB and oﬀ-axis N-NB andco-tangential P-NB are used, respectively.

Therefore, the plasma current can be overdriven without
violating the ballooning stability criterion if 11.04 MW of
co-tangential P-NB is available at JT-60SA. However, only
4 MW of co-tangential P-NB is available, therefore, onand/or oﬀ-axis N-NBs should be additionally used in orderto overdrive the plasma current.
If on- and oﬀ-axis N-NBs are injected simultaneouslywith a same total input power, the pressure gradient canbe reduced while almost the same non-inductive current isdriven. Therefore, it is better to use 4 MW of co-tangential
P-NB with two N-NBs with a necessary power for overdrive in order to avoid steep pressure gradient. However,even if 4 MW of co-tangential P-NB, 2 MW of on-axis NNB and 2 MW of oﬀ-axis N-NB are used, α/αcrit exceeds
unity at the tail of the fast ion profile. Then, a localized EC

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Fig. 8 Profiles of (a) the total plasma pressure (solid) and thefast ion pressure (broken), (b) the normalized pressure
gradient α, (c) the ratio of α over αcrit and (d) q (solid)
and the magnetic shear (broken) at 30 s and Ip = 2.1 MA.
Red, blue and Green lines represent the cases 6.42 MW of
on-axis N-NB, 7.11 MW of oﬀ-axis N-NB and 11.04 MWof co-tangential P-NB are injected, respectively.

Fig. 10 Profiles of (a) the total plasma pressure (black, solid) andthe fast ion pressure (red, broken), (b) α (black, solid) and
αcrit (red, broken), (c) q (black, solid) and the magnetic
shear (red, broken) , and (d) the bootstrap current density(red), the NB driven current density (blue) and the EC
driven current density (green) at 30 s and Ip = 2.1 MA
when 2 MW of on-axis N-NB, 2 MW of oﬀ-axis N-NB,
4 MW of co-tangential P-NB and 7 MW of EC are injected simultaneously.

5. Conclusions

Fig. 9 Dependences of max(α/αcrit ) on the input EC power on 3
diﬀerent absorption positions (black triangle: ρ ≈ 0.55,
red circle: ρ ≈ 0.65, blue square: ρ ≈ 0.70).

current drive is used in order to stabilize the infinite-n ballooning mode because αcrit becomes large if the magnetic
shear is reduced. As shown in Fig. 9, if an appropriate EC
power is applied to drive a current at just outside of the tailof the fast ion profile, α/αcrit becomes below unity. As a result, the plasma current overdrive becomes possible under
the condition that the infinite-n ballooning mode is stable
as shown in Fig. 10.

We have shown that the plasma current can beramped-up from 0.6 MA to 2.1 MA without additional CS
flux consumption using TOPICS simulation in which particle and heat transport is solved according to empiricalmodels based on the experimental results of JT-60U. Even
though, ITB in the density is weaker than the previous simulation using prescribed density profiles and the bootstrap
current decreases, the plasma current can be overdriven
within H & CD capability of JT-60SA (17 MW of NB and
3 MW of EC) if the density is decreased to fGW ∼ 0.7. The
current ramp-up rate should be very slow and it takes 330 s
for the current ramp-up from 0.6 MA to 2.1 MA. This duration is longer than discharge duration of JT-60SA, however, even lower power and slower rate current ramp-up
might be required because the infinite-n ballooning mode
is unstable in this scenario.

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In order to stabilize the infinite-n ballooning mode,the pressure profile control to obtain less steep pressure
gradient is investigated under the condition that the plasma
current is overdriven. At the low current (0.6 MA) phase,the plasma current can be overdriven without violating
the ballooning stability criterion using either 3 MW of cotangential P-NB or 7 MW of EC with the electron density
which is approximately 60% of the Greenwald limit. Even
though co-tangential P-NB can overdrive 0.6 MA with asmaller input power than EC, the pressure gradient becomes steep in wider region and the ballooning mode becomes unstable if a too much power is injected. At the highcurrent (2.1 MA) phase, a less steeper pressure profile canbe obtained when 2 MW of on-axis N-NB, 2 MW of oﬀaxis N-NB and 4 MW of co-tangential P-NB is used simultaneously and the electron density is reduced to fGW ∼ 0.3.
However, the infinite-n ballooning mode is still unstable atthe tail of the fast ion profile. Then a localized EC current drive is applied at just outside of the tail of the fast
ion profile in order to stabilize the ballooning mode by reducing the magnetic shear. As a result, it is shown that theplasma current can be overdriven under the condition thatthe infinite-n ballooning mode is stable in addition to lown ideal MHD modes if the pressure and the current profiles
are properly controlled. The required duration for CS-lesscurrent ramp-up is estimated to be longer than 500 s if the
optimized H & CD input as shown in Fig. 10 is used.

Aknowledgement

The authors wish to thank Dr. Y. Kamada for fruitful
discussion and advice on the basis of experimental knowledge in JT-60U. This work is supported by JSPS Grant-inAid for Research Activity Start-up 26889069 and carriedout under the National Centralized Tokamak Collaborative
Research Program between the University of Tokyo and
JAEA. This work was carried out using the HELIOS supercomputer system at International Fusion Energy ResearchCentre, Aomori, Japan, under the Broader Approach collaboration between Euratom and Japan, implemented by
Fusion for Energy and JAEA.
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