Plasma and Fusion Research: Rapid Communications

Volume 19, 1202025 (2024)

Initial Results of Producing Tokamak in RELAX
Takeru INOUE, Shinichiro INAGAKI, Akio SANPEI and Haruhiko HIMURA
Kyoto Institute of Technology, Department of Electronics, Matsugasaki, Sakyo Ward, Kyoto 606-8585, Japan(Received 9 April 2024 / Accepted 17 June 2024)
The safety factor and magnetic shear profiles play an important role in plasma confinement, particularly incases of nearly zero or reversed magnetic shear. This may be closely related to the formation of internal transportbarriers. We have upgraded the low-aspect ratio reversed field pinch (RFP) machine RELAX to produce tokamak
plasmas, which will be used to investigate the physics of magnetic shear within a single machine. The preliminary
measurements of the radial profile of the magnetic field have been conducted under diﬀerent conditions in two
separate experiments. The initial results indicate that standard tokamak and RFP plasmas are produced within asingle machine due to an upgraded power supply that increased the toroidal field. This unique feature enables
systematic studies of the physics of magnetic shear across the negative-to-positive region.
c 2024 The Japan Society of Plasma Science and Nuclear Fusion Research⃝

Keywords: magnetic shear, safety factor, low-aspect ratio, tokamak, reversed field pinch
DOI: 10.1585/pfr.19.1202025
In magnetically confined plasma, the magnetic structure characterized by the safety factor (q) and its spatial
derivative, i.e., the magnetic shear, is a crucial parameter
due to its vital role in plasma stability. In recent years,
non-monotonically increasing q profiles, such as nearlyflat and reversed q profiles, have garnered significant attention for use in advanced scenarios for ITER operations [1].
These profiles, known as either zero or reversed magneticshears, may improve plasma confinement through steadystate operation at high-plasma pressures and form internaltransport barriers [2]. In addition, the simulations suggest
the stiﬀness of the electron temperature profile in positive magnetic shear and the possibility of the electron temperature transport barrier in reversed magnetic shear [3].
Thus, while the relationship between turbulence and magnetic shear is studied theoretically; however, the underlying physics remain incompletely explored experimentally.
To investigate this, we plan to systematically change themagnetic shear in two toroidal magnetic configurations:reversed field pinch (RFP) and tokamak plasmas.
In RFPs, the magnitude of the toroidal field Bϕ is comparable to that of the poloidal field Bθ , and it is flipped at
the plasma periphery. These characteristics cause the magnetic field line to twist firmly, which explains the strong
negative magnetic shear. In contrast, the magnitude of Bϕin tokamaks is much larger than that of Bθ . Therefore, themagnetic shear is comparatively weak. This diﬀerence between RFP and tokamak configurations allows systematicstudies of the eﬀect of magnetic shear in toroidal plasmas.
In recent years, toroidal machines, which are initiallydesigned for RFP research, have been utilized to study
physics of tokamaks, such as runaway electrons [4] and theH-mode [5]. The power supply circuit for producing the Bϕauthor’s e-mail: d2822002@edu.kit.ac.jp

of RELAX was upgraded to form tokamaks enabling comparative studies on the eﬀect of magnetic shear profiles ina single machine, as shown in Fig. 1 (a). The aspect ratio of RELAX is the smallest among these machines [6].
Thus, RELAX should possess characteristics akin to thoseof spherical tokamaks, except that it has an iron core. Inaddition, due to the low-aspect ratio, RELAX can achieve

Fig. 1 Time evolution of (a) toroidal field coil current ITFC and(b) plasma current for typical RFP and tokamak formedin the RELAX.

1202025-1

c 2024 The Japan Society of Plasma⃝Science and Nuclear Fusion ResearchPlasma and Fusion Research: Rapid Communications

Volume 19, 1202025 (2024)

extremely deep-reversal regions [7]. This uniqueness will
enable a systematic investigation of the toroidal eﬀect ofthe magnetic shear on transport.
A tokamak in RELAX with a plasma current of 20 kA
and an edge safety factor of 4.0 yields Bϕ ≈ 0.08 T, as
shown in the red curve in Fig. 1 (b). To achieve this, thecoils were reinforced against electromagnetic solid forces
due to higher Bϕ [8]. A power supply circuit for the tokamak operation is designed to increase Bϕ . To the best of theauthor’s knowledge, this is the first study to report the formation of tokamaks in RELAX. Measured radial profilesof Bϕ and Bθ clearly indicate the successful formation of
two diﬀerent toroidal configurations in a single machine.
The profiles of Bϕ and Bθ are measured using an insertable magnetic probe array that is installed from the top
port of the chamber. The probe array consists of five pairsof pickup coils. Each pair of coils detects Bϕ and Bθ , respectively. The distance between each pair of coils in all
directions is 16 mm, corresponding to a normalized minor
radius of r/a = 0.064, where a is the minor radius. In
the experimental procedures, edge profiles of Bϕ and Bθ in
0.75 < r/a < 1.0 were investigated in detail. Figure 2 (a)illustrates the radial variation in the magnetic fields of theplasmas formed in the RELAX machine. The plots represent the time-averaged values of the measured B over flattop time in a single shot. The flat-top time is when theplasma current exceeds 80% of its maximum value.
We also draw fitting curves for Bϕ and Bθ to compre-Fig. 2 Measured radial profiles of (a) magnetic fields and (b)safety factors of typical RFP and tokamak formed in theRELAX. The probe array moves vertically toward thecenter of the vacuum chamber (R = R0 ), where R is thecentral radial coordinate, and R0 is the major radius.

hend the radial variations in the measurements. The solidand dashed curves in blue in Fig. 2 (a) depict Bϕ and Bθ
for a typical RFP, respectively. We adopted the modified
polynomial function model (MPFM), a typical model describing the equilibrium magnetic field of an RFP configuration [9]. The value of Bϕ near the wall (r = a) is negative
at approximately −10 mT. Further, Bϕ turns out to be positive (≈ 68 mT) for a typical tokamak, as recognized fromthe solid red circles.
For simplicity, based on the assumption that the setof the toroidal field coils is an annular solenoid coil, Bϕ isroughly estimated as Bϕ (R) = µ0 NIc /2πR, where R, µ0 , N,and Ic are the major radial coordinates, the permeability invacuum, the number of coil turns, and the current flowing
into the coil, respectively. All measured Bϕ must be thesame because the probe array is installed vertically from a
top port at R = R0 . Regarding Bθ , the value is calculated
based on the assumption that the toroidal plasma
current[]
jϕ distributes parabolically, that is, jϕ (r) = j0 1 − (r/a)2 ,where j0 is the current density at the center of the plasma.
Then, Bθ is given by Bθ (r) = µ0 j0 /(4a4 )(2a2 r − r3 ). The
solid and dashed curves in red in Fig. 2 (a) are obtained,
which show Bϕ and Bθ , respectively. Further, it appears
that Bϕ is approximately seven times greater than Bθ .
Finally, we calculate the radial variation of q, denotedas q(r), from the cylindrical approximation of the equationq(r) = rBϕ /(R0 Bθ ). Figure 2 (b) illustrates q(r) of a typical tokamak and the RFP. As seen from the blue curve
for a typical RFP, q(r) is less than unity, decreasing monotonically and becoming negative at the plasma periphery.
For the red curve, q(r) is greater than unity and monotonically increases from q(0) ∼ 2 at the core to q(a) ∼ 4 at theedge. These characteristics are similar to those of the standard tokamaks. Therefore, these results indicate that theRELAX has successfully formed both tokamak and RFPplasmas. The shadow region in Fig. 2 (b) will thus be theexperimental target in RELAX, which includes a flat profile of q(r) in the core.
In summary, we successfully produced circular tokamaks in RELAX to systematically study the physics ofmagnetic shear in toroidal plasmas within a single machine. The measured edge radial profiles of the magnetic
fields exhibit typical tokamak profiles in RELAX, whichwere initially constructed to produce RFP plasmas. Sucha unique feature oﬀers insights into the dependence on themagnetic shear profile of transport and equilibrium properties on toroidal plasmas. In the next series of experiments, we will control macroscopic plasma instabilities,
which provide regions akin to a low-q ∫tokamak and a highq one. In addition, we will measure ℓ ne dℓ and T e (0) by
an interferometer and a Thomson scattering.
The authors would like to thank R. Takaoka, T. Sasaki,Y. Ashida, N. Kojima, H. Fujiwara for their help in operating the RELAX, Dr. Y. Kawachi of Nagoya University
for discussions, and Dr. S. Khamaru of Kyoto Instituteof Technology for English language editing. The authors

1202025-2

Plasma and Fusion Research: Rapid Communications

Volume 19, 1202025 (2024)

would also like to thank Prof. S. Masamune of Chubu
University for fruitful discussions and Prof. M. Isobe, A.
Shimizu, Dr. S. Nakagawa, and T. Murase of the National
Institute for Fusion Science for their support. This study
was supported by grants from KAKENHI No. 23KK0053
and JST SPRING (Grant Number JPMJSP2107).
[1] ACC. Sips et al., Plasma Phys. Control. Fusion 47(5A), A19(2005).

[2] C. Gormezano et al., Nucl. Fusion 47(6), S285 (2007).
[3] Y. Idomura et al., Nucl. Fusion 45(12), 1571 (2005).
[4] S. Munaretto et al., Nucl. Fusion 60(4), 046024 (2020).
[5] G. Grenfell et al., Nucl. Fusion 60(12), 126006 (2020).
[6] L. Marrelli et al., Nucl. Fusion 61(2), 023001 (2021).
[7] R. Ikezoe et al., Plasma Phys. Control. Fusion 53(2), 025003(2010).
[8] T. Inoue et al., Fusion Eng. Des. 184, 113285 (2022).
[9] W. Shen and JC. Sprott, Phys. Fluids B 3(5), 1225 (1991).

1202025-3