J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)196–198
000–000

Current Profile Behavior during Ramping-up Phasein High Bootstrap Current Tokamak Plasmas
NAKAMURA Yukiharu, TSUTUI Hirokaki1, TAKEI Nahoko1, SHIRAI Hiroshi,
SUGIHARA Masayoshi, GRIBOV Yuri, OZEKI Takahisa, TOBITA Kenji,
TSUJI-IIO Shunji1 and JARDIN Stephen C2Japan Atomic Energy Research Institute, Ibaraki, 311-0193, Japan1
Tokyo Institute of Technology, Tokyo, Japan2
Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA(Received: 9 December 2003 / Accepted: 31 March 2004)

Abstract
Slow and quiet current ramp-up, which is necessary scenario to meet the requirements of advanced
superconducting (SC) tokamak reactor like ITER, was investigated via axisymmetric magnetohydrodynamic (MHD)
simulations. Despite the intention controlling a monotonic transition from positive shear (PS) to weak negative shear(WNS) of steady state target plasmas, cooperative link between non-inductive driven and ITB-generated bootstrap(BS) currents exhibited a self-organized recurrent appearance of PS and NS profiles. Underlying physics and operation
conditions of the newly found recurrent plasma disturbance were described in detail as well as the current profile
behaviors. Impact of the induced voltage and current on SC coils during the oscillating ramp-up and favorable scenario
to avoid and control a current hole formation are also discussed from both reactor engineering and plasma control
aspects.
Keywords:
axisymmetric MHD simulation, ramp-up scenario, bootstrap current, ITB, magnetic shear, tokamak plasma,self-organized recurrence

1. Introduction

operation, how to find the stable path to a low q regime
without collapses at a low ramping-up rate and how to avoid
and control current hole (CH) formation.

Current profile control is one of the key issue in highperformance, long pulse tokamak operations, where negative
shear (NS) plasmas tend to substantially evolve according to
the penetration of inductive currents into a core region and to
the distribution of non-inductive bootstrap (BS) currents andoff-axis LHCD [1,2]. A stable starting-up particularly requires
careful discharge controls to obtain steady state target plasmas
with weak negative shear (WNS) under certain restrictions
imposed by MHD and control aspects. For example,
superconducting (SC) tokamak reactor normally dislikes bothrunning in rapid operation and suffering plasma disturbance,
any such MHD activities as edge localized modes (ELMs).
Hence it follows that the optimization of current ramping-up
scenarios is required to attain advanced and high performance
tokamak operations.
The profile effect of the internal transport barrier (ITB)generated BS currents on the ramping-up dynamics wasstudied using Tokamak Simulation Code (TSC) [3]. Thispaper reports the simulation results on the optimization ofcurrent ramp scenarios, that is, how to establish the stable
starting-up and sustaining scenarios in the WNS long pulse

2. TSC modelingTo investigate details of the current profile behavior
during ramping-up phase, we newly installed a simple ITB
model into the TSC [4]. The ITB strength and width wereprescribed providing a functional form of the plasma pressure
profile, sharing the total pressure between the ITB and theedge transport barrier (ETB) [5]. Radial location of the ITB
foot, however, was continually adapted in accordance withthe movement of the radius of a magnetic shear reversal thatwas monitored throughout TSC simulations. Therefore, if themagnetic shear reversal lies on the magnetic axis, i.e. the PS
plasma, then the ETB bears the whole plasma pressure. On
the contrary, if the magnetic shear reversal lies on the plasmaedge, i.e. the fictitious NS plasma, then the ITB bears thewhole plasma pressure. The model of the ITB-generated BS
current was given by the expression for arbitrary values of
the aspect ratio and effective charge [6].

Corresponding author’s e-mail: nakamura@fusion.naka.jaeri.go.jp1196©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchNakamura Y. et al., Current Profile Behavior during Ramping-up Phase in High Bootstrap Current Tokamak Plasmas

currents, which gives rise to one cycle of forward andbackward transitions between the PS and NS profiles. The
mechanism can be described as following sequence: (a)External driving of substantial non-inductive current (> 20%of plasma current), (b) Formation of the NS profile, (c) ITB
formation near the NS region, (d) Growth of the ITBgenerated BS current (~ 20% of plasma current), (e) Profilemismatch of the BS and non-inductive driven currents, (f)Inward drift of the NS region, (g) Disappearance of the NS
region, (h) Disappearance of the ITB and the relevant BS
current, and finally (x) Recurrence to the PS profile.

As a reference scenario in our study, ITER-FEAT
operation scenario #4 was used, i.e., 9 MA steady state
scenario with the WNS profile of fusion power > 300 MW,
Q > 5 and the ramping-up time of ~ 24 s for 0.4–7.0 MA [7].
As for this scenario, a lot of self-consistent ASTRA [8],DINA [9] simulations have been done using feedback andfeedforward controls of plasma current and shape underpoloidal field power supply restrictions. Particular features area low current ramp rate of ~ 0.3 MA/s for reducing AC lossof SC coils, and a low Te target plasma till “start of heating(SOH)” for reducing heat load to outside limiter [7].
In addition to the ITER scenario #4, a non-inductive
current drive of ~ 20% of the plasma current was adopted inorder to attain the WNS profile. A substantial plasma pressure
which generates the BS current of ~ 20% of the plasma
current was also introduced. Thus, the fraction of ohmic
current was assumed to be low around 60%.

3.2 Evolution of magnetic shear profile during
PS to WNS transition
Figure 3 shows two examples of the recurrent evolutionsof magnetic shear profiles during the PS to WNS transition,i.e., the first one of Fig. 2 and the final one after the WNS
accomplishment of t > 10 s. As shown in Fig. 3(A), the noninductive driven current deforms local shape of the magnetic
shear to the NS around ρ ~ 0.6. Subsequently, the ITB was

3. Current profile behaviors during ramp-up
3.1 Recurrent appearance of NS region during
PS to WNS transition
Figure 1 shows time-evolutions of radial location ofmagnetic shear reversal ρs0, plasma current Ip of 0.4–7 MA,
non-inductive driven current ILH and BS current Ibs (both~ 20% of the plasma current) during a hybrid ramp-up oft = 0.0–22 s. Although the ramp-up control from the PS toWNS profiles is monotonic, a recurrent transition of NSregions appears, being not monotonic but intermittent. The
non-inductive current gives rise to the NS region around thedeposition area (ρ ~ 0.6). The ITB once formed, however,disappears soon after 1–2 s. Appearing and disappearing of
NS regions, once the WNS profile is accomplished, therecurrent appearance of the NS profile has never come backany more (later than ~ 11 s).
Figure 2 shows behaviors of the current profiles of Ip,
ILH, Ibs and the q-profile during the time period of t = 0.0–
5.5 s, that is, the first one of the recurrences. One can see acooperative link between non-inductive driven and BSFig. 1Fig. 2 Current profile behaviors of the first one of therecurrences of Fig. 1. (A) : j p, j LH; (B) j bs, safety factor q
during t = 0.0–5.5 s. Sequential mechanism ofcooperative link between non-inductive driven and BS
currents can be described as: (a) External driving of
substantial non-inductive current, (b) Formation of theNS profile, (c) ITB formation near the NS region,(d) Growth of the ITB-generated BS current, (e) Profilemismatch of the BS and non-inductive driven currents,(f) Inward drift of the NS region, (g) Disappearance ofthe NS region, (h) Disappearance of the ITB and therelevant BS current, (x) Recurrence to the PS profile.

Time-evolutions of magnetic shear reversal ρs0, plasma
current Ip, non-inductive driven current I LH at ρ ~ 0.6 andBS current I bs during ramp-up. Although the ramp-up
control from the PS to WNS profiles is monotonic, arecurrent transition of NS regions appears.

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Nakamura Y. et al., Current Profile Behavior during Ramping-up Phase in High Bootstrap Current Tokamak Plasmas

and current on SC coils during the oscillating ramp-up.
3.3.2 On a possibility of CH Formation
A strong heating after SOH (~ 22.6 s) is to be imposedon the WNS plasmas in the ITER scenario #4. Therefore,possibility of the CH formation is one of our chief concerns
relevant to the aspect of the plasma control. In order to see
whether a CH can be formed and how easily, the TSC
simulations were carried out. By changing radial locations ofthe ITBs, a strong heating was imposed on the WNS plasmas.
It was shown that it seems difficult to form a large CH of
ρ > 0.6, even when a very high BS current fraction of ~ 70%.
As the ITB region becomes smaller ( ρs0 < 0.6), the CH
becomes easy to appear. Hence, a favorable scenario to avoid
and control the CH formation can be proposed as follows:
When a sign of the CH formation is detected, 1) Quit heating,2) Expand the ITB region by controlling the deposition
position of the external non-inductive current drive.

4. SummaryFig. 3

A slow and quiet current ramp-up scenario wasinvestigated via TSC simulation for advanced SC tokamak
operational purpose. It was first shown that despite theintention controlling a monotonic transition from the PS toWNS profiles, a cooperative link between the non-inductive
driven current and BS currents exhibited a self-organizedrecurrence of the PS and NS profiles. The recurrence process
can be repeated as a sort of limit cycle, however this is notalways the case for a lower external non-inductive current
drive. Once the WNS profile is accomplished, the repeatingprocess does not appear any more.
An impact of the induced voltage and current on SC coils
was discussed from a viewpoint of the plasma disturbance
control. Furthermore, possibility of the CH formation, whichmight arise at a strong heating after SOH, was briefly
examined. Following issues are listed for future study, i.e.,model improvement of the ITB-relevant transport instead theprescribed pressure, external control to expand the ITB region
for control of the CH formation, and a similar cooperative
link between the heating profile and the ITB formation inburning plasmas.

Evolutions of magnetic shear profiles. (A) t = 1.0–5.5 s.
(B) t = 10.0–15.0 s. Non-inductive current driven aroundρ ~ 0.6, while BS current distributed around ρ < 0.6 justinside the ITB.

formed to generate the BS current distributed around ρ < 0.6
just inside the ITB. Therefore, the BS current, whose
distribution is mismatched with the non-inductive current,
drags the NS region inwards, and eventually erases it, i.e.,loss of the ITB. Thus, after retuning to the PS profile, the NSregion appears again, and then backward going to the PS.
While approaching the WNS profile in such the way, theextent of the PS inside the ITB region tends to decrease.
Consequently, after the latest formation of the NS, the PS
profile never come back anymore, that is, accomplishment ofthe WNS profile, as is shown in Fig. 3(B).

References
3.3 Discussions[1] T. Fujita et al., Nucl. Fusion 39, 1627 (1999).
[2] Y. Sakamoto et al., Nucl. Fusion 41, 865 (2001).
[3] S.C. Jardin, N. Pomphery and J. Delucia, J. Comput.
Phys. 66, 481 (1986).
[4] Y. Nakamura et al., 30th EPS Conference on Controlled
Fusion and Plasma Physics, P-2.128, St Petersburg,Russia, July 7-11, 2003.
[5] H. Shirai et al., Nucl. Fusion 39, 1713 (1999).
[6] S.P. Hirshman, Phys. Fluids 31, 3150 (1988).
[7] M. Shimada, J. Plasma Fusion Res. 78 Suppl., Chap. 14,170 (2002).
[8] R.R. Khayrutdinov and V.E. Lukash, J. Comput. Phys.
2, 106 (1993).
[9] G.V. Pereverzev et al., Nucl. Fusion 32, 1023 (1992).

3.3.1 On an impact of Recurrent NS Appearance
upon SC coils
The newly found recurrent plasma disturbances between
the PS and NS profiles may cause an additional AC loss of
SC coils of reactors in accordance with the feedback controlof the oscillating plasma position. At the every moment of
the PS and NS transitions, the induced surface voltage wasevaluated to be ~ 10 V via TSC, while the normal loop
voltage of the quiet ramping-up is < 2 V. Particularly, theradial control was shown to cause jumps of the feedback
current of ~ 50 kA. Hence, it follows that from a viewpointof the reactor engineering we have to give carefulconsideration to the additional impact of the induced voltage
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