1. Introduction
A magnetic mirror is an open magnetic system in a cylindrical geometry that suppresses longitudinal leakage through an axial mirror force exerted from the gradient of a magnetic field along the parallel direction to the field (Post Reference Post1987; Dimov Reference Dimov2005; Ivanov & Prikhodko Reference Ivanov and Prikhodko2017). In comparison with conventional experimental nuclear fusion devices such as a tokamak, mirror machines have various attractive features. Due to their simple cylindrical geometry, construction costs for the chamber are less expensive, and interpretation of the physics becomes more straightforward than with toroidal systems. High-$\beta$
plasma confinement, referring to a high ratio of plasma pressure to magnetic pressure, can be achieved in the mirror system, making mirror machines more economical. Moreover, current drive is not required for magneto-hydrodynamic (MHD) equilibrium, and therefore disruption-like events do not occur (Bagryansky et al. Reference Bagryansky, Anikeev, Denisov, Gospodchikov, Ivanov, Kovalenko, Malygin, Maximov, Korobeinikova and Murakhtin2015). Removal of helium ash, a potential problem in commercial fusion reactor operation, is intrinsically possible from the open ends of the mirror machine. Despite these advantages, mirror systems also have certain shortcomings. First, mirror systems are not MHD stable in a simple mirror geometry (Rosenbluth & Longmire Reference Rosenbluth and Longmire1957); magnetic field lines become convex at the plasma boundary in a simple mirror system; and this geometry is vulnerable to the curvature-driven flute mode (Ivanov et al. Reference Ivanov, Anikeev, Bagryansky, Bocharov, Deichuli, Karpushov, Maximov, Pod'minogin, Rogozin and Salikova1994). Second, even though an axial mirror force is applied for mitigation, significant axial loss has been observed in this open magnetic system. Because of these disadvantages, the magnetic mirror is relatively less studied compared with other mainstream device concepts for fusion energy.
Nonetheless, the shortcomings of mirror systems have been mitigated through great efforts. For stability, a minimum-|B| (where |B| is the intensity of the magnetic field) field (Hastie & Taylor Reference Hastie and Taylor1964) from the Ioffe bar (Ioffe & Kadomtsev Reference Ioffe and Kadomtsev1970) and baseball coils (Moir & Post Reference Moir and Post1969) have been added to create a concave magnetic field in the entire region, which notably prevents fluctuations due to bad curvature. Moreover, it has been reported that the interchange instability, which arises from the bad curvature, can be significantly alleviated by stimulating vortex flow at the mirror nozzle through the application of a radial electric field (Yakovlev et al. Reference Yakovlev, Shalashov, Gospodchikov, Maximov, Prikhodko, Savkin, Soldatkina, Solomakhin and Bagryansky2018). For further reduction of axial loss, the tandem mirror concept from conventional mirror systems has been applied, which provides an ambipolar potential from the mirror plasma and an additional thermal barrier from heating (Baldwin & Logan Reference Baldwin and Logan1979). Therefore, heating schemes have been developed, not only to increase the plasma temperature but also to enhance axial confinement. Thanks to these efforts, the magnetic mirror configuration has drawn more attention recently.
Currently, advanced studies are being performed to develop a fusion-based neutron source or a fusion reactor using mirror machines. Development of a continuously operating high-flux neutron source using a mirror plasma system is underway in a gas dynamic trap device with high-power (~50 MW) neutral beam injection (Bagryansky et al. Reference Bagryansky, Chen, Kotelnikov, Yakovlev, Prikhodko, Zeng, Bai, Yu, Ivanov and Wu2020). To mitigate the axial confinement loss, several confinement schemes are being tested, including a helical mirror (Sudnikov et al. Reference Sudnikov, Ivanov, Inzhevatkina, Larichkin, Lomov, Postupaev, Tolkachev and Ustyuzhanin2022) and multiple mirrors (Burdakov & Postupaev Reference Burdakov and Postupaev2018). In addition, a mirror machine applying high temperature superconducting coils for high magnetic field intensity is under construction at the University of Wisconsin–Madison (Endrizzi et al. Reference Endrizzi, Anderson, Brown, Egedal, Geiger, Harvey, Ialovega, Kirch, Peterson and Petrov2023).
Magnetic mirrors can also be utilized as a simulator of the boundary plasma in a tokamak. This is because the boundary plasma has relatively low temperature and its geometry, having a much longer axial length along the field line than its radial length, can be approximated as an open field system in a cylindrical geometry (Ohno Reference Ohno2017). Boundary plasma physics research has been conducted on several open magnetic field systems, including mirror machines, by simulating the plasma in the scrape-off layer region. Various experiments, including analysis of the detachment phenomena observed in many toroidal systems (Soukhanovskii Reference Soukhanovskii2017) and plasma–material interactions, have been performed with many mirror and linear devices such as the GAMMA10-PDX (Ezumi et al. Reference Ezumi, Iijima, Sakamoto, Nakashima, Hirata, Ichimura, Ikezoe, Imai, Kariya and Katanuma2019), NAGDIS-II (Ohno et al. Reference Ohno, Nishijima, Takamura, Uesugi, Motoyama, Hattori, Arakawa, Ezumi, Krasheninnikov and Pigarov2001) and Pilot-PSI (Morgan et al. Reference Morgan, Rindt, Van Eden, Kvon, Jaworksi and Cardozo2017).
Here, we report a new magnetic mirror device developed at KAIST (Korea Advanced Institute of Science and Technology) called KAIMIR (KAIST mirror). It is planned to be utilized for fundamental plasma physics studies, such as on instabilities and turbulence, for future application as a neutron source or for fusion energy development. This machine will also be utilized to simulate a tokamak boundary plasma in order to improve our understanding of boundary plasma physics. Thus, both mirror and tokamak boundary plasma physics can be analysed with a relatively small device providing a flexible experimental set-up and dedicated fluctuation measurements.
To initiate plasma experiments with KAIMIR, we first constructed the chamber and developed a vacuum system. A simple mirror magnetic field was implemented using a magnetic field system. A copper magnetic coil was applied to generate a maximum axial magnetic field of ~0.1 T at the centre and 0.4 T at the mirror nozzles. A plasma washer gun was utilized as the plasma source, and a probe system was utilized as the main diagnostic for electron density and temperature. The probe system includes a probe with sufficient negative-biased potential for ion saturation current measurements (I sat probe) and a probe to measure the floating potential and electron temperature (sweeping probe). A data acquisition and control system was developed with LabView software to measure the diagnostic signals and control the power system. With these developed systems, we successfully discharged plasma and conducted an initial set of experiments.
In this study, we introduce the details of the KAIMIR system and its initial operation regime in terms of electron density and temperature. Section 2 presents the overall system, consisting of a chamber and vacuum system, magnetic field system, plasma source, diagnostics and data acquisition and control system. Section 3 reports the temporally and spatially measured results of the ion saturation current (I sat), electron density and electron temperature in the reference condition. The trend of the various parameters and the radial profile change were analysed while varying the source power and the magnetic field configuration. Lastly, Section 4 summarizes our results and discusses future plans for advanced research.
2. Description of the magnetic mirror system, KAIMIR
2.1. Chamber and vacuum system
The computer-aided design model of the vacuum chamber of the KAIMIR is introduced in figure 1. The overall geometry of the device is a cylinder with a diameter of 0.5 m and a length of 2.48 m. The material of the chamber is stainless steel 316L. The vacuum chamber consists of source, centre and expander chambers with two mirror nozzles connecting them. The source chamber has a diameter of 500 mm and a length of 450 mm. In this chamber, the plasma source is installed and a single turbomolecular pump and gas injection lines are connected for pressure control. The centre chamber has a diameter of 500 mm and a length of 1180 mm. Plasma confinement in the magnetic mirror geometry takes place in this chamber. The expander chamber has the same size as the source chamber. In the expander chamber, an identical turbomolecular pump as in the source chamber and a tungsten collector plate to dump the source plasma are installed. Both the plasma source and collector plate are designed to be movable along the axial direction to adjust the stability condition of the interchange mode (Nagornyj, Ryutov & Stupakov Reference Nagornyj, Ryutov and Stupakov1984). All chambers are installed on a rail to fabricate and modify the system conveniently.
Computer-aided design model of the vacuum chamber.
To generate a high vacuum for plasma experiments with low impurities, as mentioned above, two identical turbomolecular pumps with a volume flow speed of 2000 l s−1 for He are installed at the bottom of the source and expander chambers. Both pumps are connected to a single rotary vane pump. Vacuum pressure is measured with various vacuum gauges in each chamber. A set of convection gauge and capacitance manometer is applied for low vacuum $( \ge \textrm{1}{\textrm{0}^{ - 4}}\;\textrm{Torr)}$
to atmospheric pressure measurements, and the high vacuum condition $( < \textrm{1}{\textrm{0}^{ - 4}}\;\textrm{Torr)}$
is monitored through ion gauges located on each chamber. The base pressure is ~2.0 × 10−7 Torr within this vacuum system.
2.2. Magnetic field system
The magnetic field in this device is generated through two kinds of electromagnetic coils, mirror coils and solenoid coils. Specification of the coils is shown in table 1. Two insulated-gate bipolar transistor (IGBT) switches are installed to control each coil module. By connecting the switches in parallel, the applied power to the switches can be divided. Schematic of the circuit for coil power system is introduced in figure 2(a).
(a) Coil power system schematic. (b) Simulation of the magnetic field in the R–Z plane in the reference condition (Bz ~ 0.088 T at centre, ~0.35 T at the mirror nozzle with the solenoid coil current 168 A, mirror coil current 116 A). (c) Simulated and measured Bz by axial position at R = 0 mm and simulation result of Bz by radial position.
Specifications of the mirror and solenoid coils.
The designed magnetic field is calculated using elliptic functions (Derby & Olbert Reference Derby and Olbert2010). Figure 2(b) shows the contour of the expected magnetic field intensity in typical experimental conditions with Bz ~ 0.35 T at the mirror nozzles and ~0.088 T at the centre along the R = 0 line or on-axis, corresponding to an applied current of 168 A and 116 A to the solenoid and mirror coils, respectively. We verified the magnetic field system by measuring the axial profile of the magnetic field (Bz) at R = 0. Figure 2(c) shows that the measured and calculated profiles are well matched within their uncertainties, indicating a proper fabrication and installation of the magnetic field system. From the simulation of the radial profile of Bz, the field intensity is radially uniform and the magnetic ripple is negligible $\textrm{(ripple} \equiv \delta {B_{\textrm{ripple}}}/{B_0} \le 0.03)$
in the R < 100 mm region, where most of the plasma exists during discharge. Therefore, we do not expect instabilities driven by the magnetic ripple at the edge region in this device.
2.3. Plasma source
As a high-density pulsed plasma source, a plasma washer gun is utilized (Fiksel et al. Reference Fiksel, Almagri, Craig, Iida, Prager and Sarff1996) in this device. The gun is mounted with a stainless steel pipe in the source chamber, and its axial position can be adjusted through a linear guide motion structure. The gun plasma is generated inside a washer ring between a hollow cathode and anode and then discharged to the collector plate in the expander chamber, generating a plasma column along the centre of the chambers.
Figure 3 exhibits an electrical circuit schematic of the components related to the plasma source. The source plasma in the washer gun is mainly sustained by power from a pulse forming network (PFN) system. The PFN system can provide flat, square power to the load (Rose Reference Rose2015). The PFN used in this study consists of seven segments of capacitor and inductor components. Each segment has a 1.28 mF capacitor and 0.32 mH inductor, connected in series, both connected in a ladder shape in a Guillemin type E (Rathod et al. Reference Rathod, Anitha, Sholapurwala and Saxena2014). The total characteristic impedance of the PFN system is 0.5 Ω and the pulse duration is 8.96 ms, calculated from the overall capacitance and inductance values.
Electrical circuit schematic of the PFN, sparker system and plasma source.
To initiate the plasma discharge, a sparker system generates a high-voltage spark between the gun cathode and anode. The high potential required for initial plasma breakdown is applied through a 1 : 3 transformer from the sparker capacitor. Since the potential required for sustaining a discharge is lower than the potential required for initial breakdown, the PFN system can be operated at a lower potential than required for initial breakdown with the sparker system.
Helium is used as the main discharge gas in the experiments. The discharge gas is injected for 100 ms right before plasma breakdown through a piezoelectric valve installed on the gas line in front of the plasma washer gun. The gas throughput of the valve is controlled by a maximum 100 V applied voltage from 0 to 525 sccm. The pressure at the front side of the piezoelectric valve is fixed to 3.5 bar and controlled with a pressure-regulating valve. The injection timing and duration are adjusted by the trigger signal from the data acquisition and control system, which is described in § 2.5.
Figure 4 shows the temporal evolution of the voltage and current in the PFN circuit applied to the washer gun under the reference discharge condition. After ramp up in ~1 ms after the triggering of the sparker, the voltage and current applied to the plasma gun are maintained until ~4 ms. Afterwards, a small hump in the signal with a height of ~10 % is observed in both voltage and current signals from 4 to 7 ms. After 7 ms, the voltage and current signals start to decay and fall off to 0 at ~12 ms. The measured values are compared with the circuit simulation results, as shown in figure 4. The signal levels during the steady period (1–4 ms) agree well, indicating that the PFN system works as designed. However, some discrepancies remained. In the simulation, the gun current fluctuates in contrast to the experiment. This is because we simply assumed the load as a resistor. In the experiment, the circuit is opened when the plasma is turned off, so the current flow becomes 0. Then the discharge voltage shows ringing in the experiment, dissipating the remaining energy in the PFN circuit. Also, the circuit simulation does not predict the hump observed in the experiment in the 4–7 ms period. This difference can be attributed to the impedance mismatch between the PFN circuit and the plasma in time. Different rise and fall times can be related to slight differences in the estimated stray resistance.
Temporal evolution of (a) discharge voltage and (b) gun current in the reference condition experiments and circuit simulation.
2.4. Langmuir probe system
A Langmuir probe is a versatile tool that can measure the electron density, electron temperature and electron energy distribution from the characteristics of the current flowing from the plasma to the metal probe tip under arbitrary biased voltage (Chen Reference Chen2003). Cylindrical Langmuir probes were fabricated to measure I sat at a fixed negative voltage and to acquire current–voltage (I–V) curves by sweeping the biased voltage for electron temperature measurements.
The structure of the Langmuir probe consists of a tungsten metal tip, alumina tube, ceramic tip and a stainless steel 316L (SUS316L) tube, as shown in figure 5(a). The alumina and SUS316L tube, used to sustain the structure and protect the wire from the plasma, are connected mechanically. The length of the tungsten tip exposed to the plasma is ~1 mm, with a diameter of 0.3 mm. Figure 5(b) shows the axial locations of the probes used in this study. Probe measurements are performed mostly near the centre of the system, Z ~ 0.06 m. We also inserted a probe at the mirror nozzle near the plasma source to monitor changes in the source region, Z ~ −0.69 m, during the experiment.
(a) Drawing of the Langmuir probe structure. (b) Axial locations of the probe measurements.
The value of I sat is monitored by measuring the probe current with a negative-biased voltage sufficient for ion saturation current measurements. A bias voltage of −150 V is supplied in most cases by a linear DC power supply, which is determined from current measurements from the sweeping probe. The value of I sat is measured by using a shunt resistor and isolation amplifier, as shown in figure 6(a). To acquire the I–V characteristic curve for electron temperature measurements in the sweeping probe circuit, a voltage amplifier is added, as shown in figure 6(b). A triangular waveform with a 10 kHz sweeping frequency is generated from a developed data acquisition and control (DAC) system for voltage sweeping, and it is amplified through the voltage amplifier with a gain as high as 10. The probe current with the swept voltage is measured by the shunt resistor, as used in the I sat measurements. The swept voltage is monitored by 1 : 10 probe. In the time trace of the voltage and current, the triangular waveform of the swept voltage became distorted when the probe current reached the limitation of the voltage amplifier, as shown in figure 6(c), because of the high plasma density. Because of this limitation, the I–V curve was obtained in the ion saturation region and transition to the electron saturation region. To remove the possible distortion of the I–V curve in the transition region, we excluded the distorted points in the fitting of the I–V curve. Electron temperature is estimated by averaging the values from 10 I–V curves. We can notice that the resulting I-V curve follows the exponential fitting properly, as shown in figure 6(d). From the estimated electron temperature and measured I sat, the electron density is estimated from the Bohm formula, ${n_e} = {I_{\textrm{sat}}}/{e^{ - 0.5}}{A_p}{q_e}\sqrt {k{T_e}/{M_{\textrm{ion}}}}$
, where e is base of the natural logarithm, Ap is area of the probe surface, qe is electric charge of electron, Te is electron temperature and Mion is mass of the ion (Chen Reference Chen2003). We note that the Bohm formula is valid for a planar probe, as the ion current does not saturate in the cylindrical probe due to the sheath expansion from the bias voltage, since total sheath thickness is $d = [{\textstyle{2 \over 3}}{(2{q_e}{V_0}/k{T_e})^{3/4}} + 5]{\lambda _{\textrm{Debye}}}$
, where d is sheath thickness, V 0 is voltage between probe and plasma and λDebye is Debye length. However, since the measured electron density is high (>1019 m−3) in our system, the ratio of the probe size to the Debye length, ${\xi _p}( = {r_p}/{\lambda _{\textrm{Debye}}})$
with probe radius, rp, is sufficient (exceeding >56) to use the Bohm formula where the Laframboise curve shows saturating trends for the bias voltage (Chen Reference Chen2001). Based on this estimate, the Bohm formula was utilized in this study. However, it is noteworthy that the I sat level can still be overestimated by 60 % due to the sheath expansion at relatively low density (<1019 m−3). We therefore need to perform an additional analysis to interpret I sat measurements when the plasma density is low.
Panels show (a) I sat, (b) sweeping probe circuit schematics, (c) sample voltage and current time traces and (d) I–V curve.
2.5. Data acquisition and control system
We developed the DAC system for triggering and controlling the power systems and acquiring the diagnostic signals based on LabView software. Specific timings of the triggering for diagnostics and control are shown in figure 7. The digital output signal from the DAC is converted to an optical signal in an electro-optic transceiver for electrical isolation of the power and signal lines. This system also synchronizes and controls the on/off timing of the relay and the IGBT switches in the coil power system, the IGBT switch for the sparker system and the piezoelectric valve in the gas injection system. Voltage and current measurements to monitor the PFN and coil power systems are performed with a relatively low sampling rate, 0.1 MS s−1 (=0.1×106 samples per second) and Langmuir probe signals are measured with a relatively high sampling rate, 2.0 MS s−1.
Specific trigger signals with time to control the magnetic coils, plasma gun and gas.
3. Results of the initial plasma experiments with the KAIMIR system
We initially investigated the fundamental plasma parameters and the operation regime of He discharges in KAIMIR. We verified that the discharge is reproducible within 10 % by measuring the on-axis I sat at Z ~ 0.06 m, where Z = 0 is the axial centre of the system, as shown in figure 5(b), in the reference discharge condition, which is explained in the following section. Using the reproducibility of the discharge, spatial profile measurements were performed in a shot-by-shot basis.
3.1. Characteristics of the plasma in the reference discharge condition
The reference discharge condition refers to the typical discharge conditions in KAIMIR experiments, defined as the following adjustable system variables: magnetic field configuration, PFN voltage, sparker voltage, gun location and gas injection timing and duration. The reference condition is summarized in table 2. We first investigated the characteristics of the plasma generated in the reference condition.
System variables for the reference condition and their ranges in the KAIMIR experiments. The trigger timing of the IGBT switch for the sparker system is referenced as 0 ms, and the centre of the vacuum chamber is referenced as the 0 m axial position.
In the reference condition, magnetic field amplitudes were set to 0.088 T and 0.35 T at the centre and mirror nozzles, respectively. Thus, the mirror ratio, defined as the ratio of maximum and minimum magnetic fields in the mirror plasma, is around 4 in this condition. The PFN voltage for the reference condition was set to 0.5 kV, the middle of the adjustable voltage range (0–1 kV). Trigger voltages were set to sufficient levels for initial breakdown, varying from 3.5 to 4.0 kV. We confirmed that variation in the trigger voltage did not affect the plasma performance. Gas throughput and injection timing were set to 490 sccm from −100 to 0 ms, where 0 ms refers to the time when the plasma starts to discharge by applied trigger voltage. Axial positions of the source and collector plate were fixed to Z = −0.9 m and 1.0 m, respectively.
Figure 8 shows the temporal evolution of the source power (PFN power) and probe measurement results including I sat, electron density and electron temperature. It can be noticed in figure 8(a) that steady power is supplied to the plasma gun during discharge, as expected from figure 4. After triggering, PFN power was maintained until ~4 ms, after which it slightly increased during 4–7 ms. After 7 ms, the power decayed to 0 by ~12 ms. Figure 8(b) shows I sat measured by the probe located on-axis (R = 0, Z = 0.06 m). The current was low pass filtered (f cutoff: 10 kHz) to see the trend of the parameters. We also observed the floating potential measured by the sweeping probe at the same location. The values of I sat and floating potential stayed at ~0.05 A and −58 V, respectively, during 1–7 ms. After 7 ms, I sat decreased exponentially, following the decay of the source power. The absolute value of the floating potential was also reduced in this period; this reduced value could be due to the reduced seeded electrons from the gun at lower PFN powers. The electron temperature measured by the sweeping probe was ~4–7 eV during 1–7 ms, as shown in figure 8(c). Based on I sat and the electron temperature, we estimated the electron density. As shown in figure 8(d), the density level was ~4.5 × 1019 m−3 in the same time range (1–7 ms). In the decay phase (>7 ms), the reduction of I sat was mainly due to changes in the electron density, rather than the electron temperature, since it was observed that the density was reduced more abruptly than the temperature. It is also worth noting that the decaying slope of the PFN power is steeper than the slope of I sat or electron density. Applying exponential fitting $({\sim} {C_1}exp ( - t/{\tau _{\textrm{decay}}}) + {C_2})$
in the 8–11 ms decay phase, we observed that the characteristic decay time $({\tau _{\textrm{decay}}})$
of the power is ~0.6 ms while the decay time of I sat is ~1.6 ms. Considering the possible overestimation of the I sat level due to the sheath expansion at low density, the exact decay time of I sat can be shorter than the obtained level. The estimated time considering this effect is ~1.4 ms, which is still longer than the decay time of the power. This difference shows that the plasma was sustained even after the power was turned off, which could represent the confinement efficiency.
Temporal evolution of (a) source power, (b) I sat, floating potential (Vf), (c) electron temperature (Te) and (d) electron density (ne) on-axis (Z = 0.06 m) in the reference condition.
From the on-axis electron density and temperature of the plasma, the main physical parameters of the plasma were estimated as shown in table 3. Operation pressure is the neutral pressure during the discharge, and it was estimated under the assumption of a uniform pressure inside the chamber with the equation $Q = {V_{\textrm{chamber}}}(\textrm{d}{P_{\textrm{chamber}}}/\textrm{d}t) = {Q_{\textrm{gas}\;\textrm{injection}}} - {P_{\textrm{chamber}}}{S_{\textrm{pump}\;\textrm{speed}}}$
, where ${V_{\textrm{chamber}}}$
is the overall volume of the vacuum chamber, ${Q_{\textrm{gas}\;\textrm{injection}}}$
is the flow rate of the gas injection line and ${S_{\textrm{pump}\ \textrm{speed}}}$
is the total pumping speed of the pump system. The calculated pressure was 0.95 mTorr, which is in accordance with the measured pressure by ion gauge (~1 mTorr). This pressure corresponds to the neutral density 3.1 × 1019 m−3 at room temperature. Because ion temperature measurements are not available at this point, Ti was assumed to be 10 % of Te from previous studies performed under similar conditions, including electron density and temperature levels, and thus a similar energy transfer rate from electrons to ions by collision (Thakur et al. Reference Thakur, Gosselin, McKee, Scime, Sears and Tynan2016; Arakawa et al. Reference Arakawa, Inagaki, Sasaki, Kin, Hasamada, Yamasaki, Kobayashi, Yamada, Nagashima and Fujisawa2019). As the ion and electron Larmor radii are much smaller than the scale of the current system, the plasma was magnetized in these initial experiments. The electron–ion and ion–ion collision frequencies are high enough to satisfy the condition, $L \gg {\lambda _{\textrm{ii}}}(\ln {R_M}/{R_M})$
, which indicates that the KAIMIR plasmas are in the gas dynamic regime (Ivanov & Prikhodko Reference Ivanov and Prikhodko2017). Based on the estimated neutral pressure, the electron–neutral collision frequency $(\nu _0^{e/n})$
and its mean free path $\textrm{(}\lambda _{\textrm{mfp}}^{e/n})$
were also calculated based on the electron–neutral total cross-section data (Raju Reference Raju2018). As collisions of electrons with ions and electrons lead to the diffusion of the electrons, collision events with neutrals also play a role in the diffusion. However, based on the comparison of collision frequencies, electrons will be diffused mainly by the collisions with the charged particles.
Main plasma parameters in the reference condition. Here, $\nu _0^{s/s^{\prime}}$
is the collision frequency from species s to s’, and $\lambda _{\textrm{mfp}}^{s/s^{\prime}}$
is the mean free path of collision from species s to s’.
3.2. Effect of source power
To check the operation regime, the on-axis electron density and temperature of the plasma at Z ~ 0.06 m were measured while scanning the source power (PFN power). In this experiment, the source power was varied by adjusting the PFN voltage from 0.2 to 0.9 kV.
Probe measurements were done at (R, Z) = (0, +0.06 m). Figure 9(a) shows the changes in I sat with the source power. The I sat level increased with the source power and its growth was alleviated with the source power. As shown in figures 9(b) and 9(c), we observed that the electron density increased from 1.3 × 1019 to 1.0 × 1020 m−3 while the electron temperature remained at a similar level of 5–6 eV during the power scan. It is noteworthy that the increase of the electron density level was mitigated at high source power, over 0.2 MW, similar to the behaviour observed in the I sat measurements. Therefore, the trend observed in I sat was mainly attributed to changes in the electron density with source power.
Panels show (a) I sat, R = 0 mm, Z = 0.06 m, (b) ne and (c) Te with varying source power. The data are averaged in the range 4–7 ms.
The similar levels of electron temperature observed during the power scan experiment can be explained by the plasma generation mechanism in KAIMIR. Plasma in this device is mainly generated from collisions between background neutrals and electrons emitted from the washer gun. The electron–neutral impact ionization cross-section from the ground has a threshold at 24.6 eV and rapidly increases with higher electron temperature (Ralchenko et al. Reference Ralchenko, Janev, Kato, Fursa, Bray and De Heer2008). It is expected that ionization of the background plasma is driven by the tail of energetic electrons or via multiple successive impact excitations. Because the density and temperature of the initial seed electrons increase at higher source power, the ionization rate affecting the density of the main plasma increases. However, to increase the electron temperature of the main plasma, the energetic electrons from the gun should be thermalized through Coulomb collisions with the background electrons. Since the Coulomb collision frequency with the energetic electrons is inversely proportional to cube of the velocity of energetic electrons from the gun, higher source power can be ineffective in increasing the temperature of the background electrons.
Radial profiles of the electron density and temperature were measured at PFN voltages of 0.3, 0.5, 0.7 and 0.9 kV in the range R = 0–50 mm. The electron density over all radial positions increased with the source power. It also tends to decrease as it moves radially outward. Here, electron density could be overestimated at the periphery region (R > 30 mm) similar to the decaying phase in § 3.1, which will make the profile steeper than the measured one. The density profile was fitted with a Cauchy distribution $({n_e}(r) = (2A/\pi )(w/(4{r^2} + {w^2})))$
to evaluate the effective radius of the plasma. In the fitting, the characteristic length of the radial profile (w) increased by 20 % while varying the source power from 0.03 to 0.28 MW. This demonstrates that the radial profile broadens as the source power increases. Stored electron energy per unit length at Z = 0.06 m, which refers to the integrated energy density over the area in this study, was calculated from these profiles to estimate the trend of overall stored energy of the plasma. To calculate the stored electron energy, the radial profiles of the electron density and temperature were integrated with assumed azimuthal symmetry, ${W_e}/L = 2\pi \int_0^R {{\textstyle{3 \over 2}}{n_e}{k_B}{T_e}r\,\textrm{d}r}$
, as shown in figure 10(b). In this estimation, R, the plasma radius, was determined to be 50 mm. The slope of the stored electron energy decreases as the source power increases, consistent with the trend of ne observed in figure 9(b). The estimated energy can be decreased up to 30 % considering the overestimation of the probe due to sheath expansion. However, the observed trend will still be valid since this effect is more significant for the case with the lower source power.
(a) Radial profile of ne with the measured data and the fitted curve (dashed line) with a Cauchy distribution, and (b) the stored electron energy at Z = 0.06 m with varying source power.
The decrease of the slope of the stored electron energy represents the fact that the stored energy of the plasma does not follow the source power linearly. This trend can be attributed to the reduced confinement time with the source power. If higher source power increases the ion temperature of the plasma, this will reduce the axial confinement time, according to the gas dynamic trap scaling, ${\tau _{\textrm{GDT}}}\sim {R_M}L/{V_s}$
. It is also possible that radial transport is enhanced with the source power due to a certain instability. Further investigation will be performed to understand the observed trend.
3.3. Effect of the mirror ratio
The mirror ratio is known to affect axial confinement significantly in mirror machines (Soldatkina, Bagryansky & Solomakhin Reference Soldatkina, Bagryansky and Solomakhin2008). In the present work, the magnetic field intensity at the mirror nozzles increased from 0.14 to 0.35 T while the field intensity at the centre (Z = 0) remained at 0.07 T, as shown in figure 11(a). Consequently, the mirror ratio of the system varied from 2 to 5. During the scan, the source power was maintained to 0.87 MW. To check the changes in the source region by the magnetic field intensity at the mirror nozzle between the source and centre chambers, we observed the trend of I sat at the source nozzle near the plasma gun. As shown in figure 11(b), I sat, source nozzle is almost constant at different mirror ratios, while I sat, centre increases with the mirror ratio. This indicates that the increased I sat, centre is not due to changes in the source region. Figures 11(c) and 11(d) show the variations in the electron density and temperature with the mirror ratio. The electron density increases almost linearly with the mirror ratio, which could be related to enhanced confinement due to the reduction of axial leakage at higher mirror ratios.
(a) Axial profile of the magnetic field intensity for mirror ratios of 2–5, (b) I sat, source nozzle and I sat, centre, (c) ne and (d) Te on-axis at different mirror ratios (RM). The data are averaged in the range 4–7 ms.
Figure 12(a) shows the radial profiles in the mirror ratio scan experiment. Results show that electron density increases with the mirror ratio at all radial locations. The density profile was fitted with the same Cauchy distribution used in the power scan analysis (§ 3.2). The characteristic length of the radial profile remained within values below 10 %, which indicates that the shape of the radial profile was almost constant while varying the mirror ratio. The same calculation process performed in the source power scan was applied to calculate the stored electron energy. It was found that the stored electron energy almost linearly increased with the mirror ratio, as shown in figure 12(b). This trend was also identical when the sheath expansion is considered in the probe measurements. The linear increase of the stored electron energy with mirror ratio while maintaining the source power suggests that the plasma confinement is enhanced with the mirror ratio. This trend is consistent with the confinement time scaling in the gas dynamic regime, ${\tau _{\textrm{GDT}}}\sim {R_M}L/{V_s}$
, which can be expected from the high collision frequencies shown in table 3.
(a) Radial profile of ne with the measured data and the fitted curve (dashed line) with Cauchy distribution, (b) the stored electron energy at Z = 0.06 m for different mirror ratios (RM).
4. Summary and future work
A new linear magnetic mirror device called KAIMIR was constructed and initial experiments were conducted. In the device, plasma is generated in pulsed mode with a plasma washer gun and a mirror geometry magnetic field is generated from a coil power system. The maximum magnetic field intensity is 0.1 T at the centre and 0.4 T at the mirror nozzles. The source power of the plasma gun is supplied by a PFN system with a duration of ~10 ms. Data acquisition of diagnostics as well as system triggering and synchronization are performed with a DAC system. Through a series of initial experiments, we measured the electron density and electron temperature in diverse conditions and determined the possible range of electron density and temperature levels in this system. The on-axis electron density could vary from 1.3 × 1019 to 1.0 × 1020 m−3 and the electron temperature in the range 4–7 eV by the source power. These values are in a similar range to those of other devices used to conduct edge plasma physics studies (Ohno Reference Ohno2017). The electron density also linearly increases with the mirror ratio, consistent with gas dynamic trap scaling. This result is attributed to the system's high density and low temperature, i.e. high collision frequency, which allows experiments to be conducted in the gas dynamic trap regime.
From the set of initial experiments, we were also able to identify a number of required improvements. First, an external heating system needs to be added. We observed that increasing the source power is not effective to increase the electron temperature. Higher temperatures will be needed to simulate conditions closer to a tokamak boundary plasma. It may also be beneficial to consider varying collisionality in studying plasma physics. For these reasons, we will install an electron cyclotron heating system and ion cyclotron heating system in the near future.
Second, plasma stabilization will be required to enhance plasma performance. Previous studies showed that it was essential to suppress the MHD instabilities for better confinement (England et al. Reference England, Lee, Lee, Kwon, Yoon, Yasaka, Sugimoto, Katanuma, Yashiro and Imai2009; Ryutov et al. Reference Ryutov, Berk, Cohen, Molvik and Simonen2011; Qing et al. Reference Qing, Guanghui, Baoming, Jiacheng, Zhida and Xuan2023). In the near future, we will scan the location of the collector to adjust the stability of the interchange mode. We will also utilize the vortex flow scheme (Beklemishev et al. Reference Beklemishev, Bagryansky, Chaschin and Soldatkina2010) to suppress the radial transport driven by MHD instabilities.
Third, to estimate the particle and energy confinement times, we need to improve the experimental conditions and measurements, as follows. In this study, we initially calculated the stored electron energy during the stationary period. To estimate the energy confinement time from the power balance equation, it is required to estimate the radiative energy loss and the loss due to collisions with neutrals as well as the energy stored in the plasma. For the radiative loss, although bremsstrahlung power is expected to be much lower than other loss mechanisms such as axial loss, line radiations also contribute to radiative loss. Therefore, radiative loss power should be checked using a bolometer in the future. To calculate the energy loss due to collisions with neutrals, the density of the metastable states of the neutral atom is necessary. We will utilize the collision–radiative model to calculate the density of the metastable states. To estimate the particle confinement time, we will develop diagnostics measuring particle flux at the expander chamber. In addition, the confinement time can be estimated from the decay time of the plasma when the source power is turned off. Although we observed a longer decay time in I sat than the power decay time, we did not utilize this decay time to estimate the energy confinement time since the decay time of the source power (~0.6 ms) is similar to the decay time of I sat (~1.6 ms) in the current system and the I sat level, ~neTe 1/2, does not indicate either the exact particle or energy level. To analyse the confinement time in the decay period, the power decay time should be shorter than the estimated confinement time. We plan to add a switching circuit to actively control the current flow to the plasma source and shorten the decay time in the future. We will also install an interferometer and a diamagnetic loop for the plasma density and energy measurements, respectively. These diagnostics will be utilized to estimate the confinement time in the near future.
Acknowledgements
Editor Cary Forest thanks the referees for their advice in evaluating this article.
Funding
This work was supported by the National Research Foundation of Korea (NRF) funded by the Korean government (Ministry of Science and ICT) (RS-2023-00212124, RS-2022-00155956) and by an internal project funded by the Korea Advanced Institute of Science and Technology (KAIST) (N10230029, N10230137). I.K. gratefully acknowledges financial support from Khalifa University via the (internally funded) grants (FSI-2021-012/8474000352, CIRA-2021-064/8474000412).
Declaration of interests
The authors have no conflicts to disclose.
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