Plasma and Fusion Research: Regular Articles

Volume 14, 3402116 (2019)

Soft X-Ray Measurement on the Collisional Merging Process
in a Field-Reversed Configuration∗)
Junichi SEKIGUCHI, Tomohiko ASAI and Tsutomu TAKAHASHI
College of Science and Technology, Nihon University, Tokyo 101-8308, Japan(Received 10 January 2019 / Accepted 7 May 2019)
To investigate excited shockwaves in a collisional-merging field-reversed configuration (FRC), soft X-ray(SXR) measurement was initiated on the FRC amplification via translation collisional merging (FAT-CM) instrument. Since the FRCs collide at a relative speed of 300 - 400 km/s on the FAT-CM, which is faster than theAlfvén velocity in the separatrix, shockwaves are assumed to be excited in the colliding FRCs. These excited
shockwaves would play an important role in energy conversion during the collisional merging formation processof the FRC. The relation between the global behavior of the FRC in the collisional merging process and the time
evolution of SXR signals are discussed herein.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: field-reversed configuration, shockwave, collisional merging, super-Alfvénic translation
DOI: 10.1585/pfr.14.3402116

1. Introduction
Compact torus (CT), such as field-reversed configuration (FRC) and spheromaks, have toroidal magnetic configuration with simply-connected geometry [1]. A CT canbe accelerated by a magnetic pressure gradient and translated axially. This translation technique provides the separation of the formation and burning sections in the reactor in order to fuel the reactor core plasma and perform
merging of the CTs. Spheromak-merging experiments [2]show the energy conversion in which the magnetic energy of spheromaks is converted into the thermal energyof a merged FRC thorough magnetic reconnection. Collisional merging of two FRCs at super-Alfvén velocity wasperformed on the C-2/C-2U device [3]. In the collisional
merging experiments, axial kinetic energy is converted
mostly into thermal ion energy of the merged FRC plasma.
Although FRC by collisional merging formation shows
significantly higher performance compared with singletranslated FRC, the details of the collisional merging process are unclear.
In order to investigate the collisional merging processof FRC at super-Alfvén velocity, the FRC amplification via
translation (FAT) device was recently upgraded to a FAT
collisional merging (FAT-CM) [4]. In this work, since theFRCs collide at a relative axial velocity of 300 - 400 km/s,
which is faster than the Alfvén velocity in the separatrix,
shockwaves are assumed to be excited in the colliding
FRCs. Excited shockwaves would play an important rolein the energy conversion during the collisional merging
formation process of FRC [5]. Shock-based heating is theauthor’s e-mail: sekiguchi.junichi@nihon-u.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

most eﬀective mechanism in plasmas, with most ions in thefield-reversed theta-pinch (FRTP) formation process [1].
In the FRC translation experiment on the FRC Injection
Experiment (FIX), FRC plasma translated into mirror magnetic field at super-Alfvén speed was re-thermalized bycollision-less shockwaves [6]. A similar heating process
could occur in the collisional merging process on the FATCM. To investigate the excited shockwaves in the colliding
FRCs, soft X-ray (SXR) measurement was attempted on
the FAT-CM. The relation between the global behavior of
the FRC in the collisional merging process and the time
evolution of the SXR signal are discussed.

2. Experimental Device
Figure 1 shows a schematic diagram of the FAT-CMdevice. The device comprises two FRTP formation sections as FRC sources and a central confinement vesselto perform collisional merging. The formation sections
are called “R-formation” and “V-formation,” respectively.
Deuterium gas is introduced via gas-puﬀ valves mounted
at the ends of both formation sections. Quasi-static magnetic confinement field coils are placed along the confinement section. Details of the FAT-CM parameter and basic
diagnostic are described in the reference of [4].
Figure 2 shows a schematic diagram of the SXR measurement, with three beryllium film filters installed at themidplane of the confinement vessel. A negatively biased
voltage of 45 V was applied to a silicon surface barrier detector (ORTEC, BU-012-50-100) [7] with an aﬀective areaof 50 mm2 , by a battery. Visible light was blocked using aberyllium film of φ18 mm. Thus, bremsstrahlung radiationin the range of SXR from the plasma is detected [8]. Since
two of the beryllium films are retractable, the total thick-3402116-1

c 2019 The Japan Society of Plasma
Science and Nuclear Fusion ResearchPlasma and Fusion Research: Regular Articles

Volume 14, 3402116 (2019)

Fig. 1 Schematic diagram of the experimental device FAT-CM.

Fig. 2 Schematic diagram of the SXR measurement.

ness can be switched to 12.5, 25, or 37.5 µm. To limit thefield of view, indicated by light blue in Fig. 3, a stainlesssteel disk (SS304, 1-mm thick) with a φ10-mm hole wasmounted. The thickness of the beryllium film was fixed at
37.5 µm in the present work.

3. Experimental Results
Figure 3 shows the time evolutions of the excluded
flux radius, the double-passed, line-integrated electron
density, the total temperature, and the output signal of theSXR detector measured at the midplane of the confinement section. In this series of experiments, two individually formed FRCs, whose radius, length, electron density, and total plasmoid temperature are about 5 cm, 0.6 m,
2 × 1021 m−3 , and 110 eV, respectively, and collide aroundthe midplane at a relative axial velocity of 300 - 400 km/s.
The FRC expands in volume in the collisional merging process and settles into an equilibrium state.
The three phases of the collisional merging process
are defined as shown in Fig. 3. In phase 1, the volume ofthe plasmoid rapidly increases mainly due to radial expansion. The length of the plasmoid ranges from 1.5 - 2.0 m
during the collision, merging and equilibrium phases. The
line-integrated electron density and the SXR signal also increase during phase 1. The SXR signal amplitude can beassumed to be T e0.5 n2e exp{−E/T e }T (E)dE, where T (E)is the transmission function determined by the metallic fil-Fig. 3 Time evolutions of (a) the contour of excluded flux radius, (b) the excluded flux radius, (c) the double-passed,
line-integrated electron density, (d) the total temperature and (e) the SXR signal for a typical merged FRC(#11049).

ter and the absorption function of the detector [9, 10]. The
peak of the excluded flux radius profile is flattened in thephase 2. The SXR signal transits to a modestly increasingphase, defined as phase 3. Here, T t is calculated from thepressure balance as
T t = T e + T i = βB2e /2μ0 kB ne ,(1)β = 1 − 0.5(rΔφ /rt ) ,(2)2where β, Be , μ0 , kB , ne  and rt are the average beta,
external magnetic flux density, permeability, Boltzmann
constant, average electron density and wall radius, respectively.
Figure 4 shows ΔB (= Bp − Bv ), which is the diﬀerence of the external magnetic field with and without thecolliding plasmas, measured by an array of pick-up coils
installed on the inside-wall of the confinement vessel. The
ΔB corresponds to the excluded flux Δφ = (rΔφ /rt )2 Bp .
The relative velocity of the colliding FRCs is estimated3402116-2

Plasma and Fusion Research: Regular Articles

Volume 14, 3402116 (2019)(a) Ion-ion collision time

Fig. 4 Time evolution of the external magnetic field on the collisional merging process (#11049).

(b) Electron-ion collision time
as 370 km/s using the time-of-flight method with the magnetic field, and is indicated by dashed lines in Fig. 4 inphase 1. The Alfvén velocity in the FAT-FRC is roughly 80
km/s, calculated from the experimentally measured lineintegrated electron density and the external magnetic field.
Although this Alfvén velocity is not estimated locally, theAlfvén Mach number would be greater than 4 in the separatrix, because the internal magnetic field of the FRC generally shows a trend to decrease toward a magnetic axis.
A significant hump in the excluded flux, which is probably caused as the result of generated shockwaves, is observed around the midplane of the confinement vessel [11].
The dashed lines after the collision in phase 2 indicate a
propagating hump in the excluded flux radius. The humpoccurs due to increased pressure via the process of rethermalization of ion kinetic energy into thermal energy.

4. Discussion
The thermal relaxation time is evaluated to compare
the time evolution of the SXR signal. Ion-ion and electronion collision time for the formed FRC plasma parameters
are calculated as shown in Fig. 5. The ion-ion collisiontime in the FRC is about 10 µs, which is comparable to theduration of phase 2 in Fig. 3. The electron-ion collisiontime is shorter than the time scale of the global motion in
the collisional merging process. This indicates that the axial ion momentum is thermalized by the ion-ion thermal
equilibrium in phase 2. Then the electrons in the merged
FRC are heated by ion-electron collision until reaching
thermal equilibrium. In phase 3, the total temperature decreases but the SXR signal amplitude increases. This isFig. 5 Collision time calculated by the FAT-FRC plasma parameters.

because ion-electron thermal relaxation time is faster than
the time scale of decreasing T t . The time evolution of theion or electron temperature up to thermal equilibrium isshown as below [12]:T t = T e + T i : (T i > T e ),dT e
1=(T i − T e ),
dt
τeq

(3)
(4)

where τeq is the energy equilibration time between ions andelectrons. Although the ratio of ion temperature and electron temperature is not estimated, ion temperature would
be much higher than electron temperature given the shockheating.
The transition of the internal magnetic field profilein the collisional merging process was experimentally observed on the FAT-CM [13]. The internal magnetic field
profile was experimentally observed by an array of pickup coils installed at the midplane where the SXR detector
is mounted. The SXR and internal magnetic field profiles
were not measured at the same time because the field ofview was intercepted by the array. The internal magnetic
field structures in phase 1 (at 46 µs), and in phase 2 (at80 µs), have a clear, field-reversed structure. At phase 1,a strong Bt field is observed. The local toroidal magnetic
field component could be measured by a shift or tilt motion of the FRC containing no toroidal magnetic flux [14].
Moreover, toroidal magnetic flux can be generated by the3402116-3

Plasma and Fusion Research: Regular Articles

Volume 14, 3402116 (2019)

FRC translation process [15]. The observed Bt field profile evolution and the change in direction indicate a plasma
motion/shift in axial direction. In phase 2 (at 80 µs), there
remains a modest Bt field without changing of positive andnegative signs. The reversed Bp field in phase 2 shows
good agreement with the rigid rotor profile model [1],which is commonly used to model the poloidal flux structure during the equilibrium phase. The time scale of thetransition of the internal magnetic field profile is also comparable to the risetime of the SXR signal.

5. Summary
The newly installed SXR measurement on the FATCM showed a relation between SXR intensity and global
motion during and after the collisional merging process oftwo FRCs. The axial ion momentum is likely to be thermalized by the ion-ion equilibrium once the calculated ionion collision time is comparable to the duration of the risetime of the SXR intensity.

Acknowledgement
This work was supported in part by a Grant-in Aid for
Scientific Research JP16K06939 from the Japan Society
for the Promotion of Science (JSPS).
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