2 Experiments and theoretical background

As a theoretical basis in the manuscript, a value of $W$ is defined as a key parameter and a measure of velocity shear in rotating plasmas with radially non-uniform plasma density (for more detail, see figure 1). The axial $(z)$ component of normalized dynamic vorticity $W=[\unicode[STIX]{x1D735}\times (n\boldsymbol{V}_{E})]_{z}/n_{0}=d/dr_{c}[nr_{c}^{2}\unicode[STIX]{x1D6FA}]/(n_{0}r_{c})$ (where $n_{0}$ is the on-axis density) is chosen to characterize $\boldsymbol{E}\times \boldsymbol{B}$ velocity $(\boldsymbol{V}_{E})$ shear). (Pastukhov Reference Pastukhov2005; Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a , Reference Cho, Hirata and Pastukhov2006). The rotational frequency $\unicode[STIX]{x1D6FA}(r_{c})$ characterizes the azimuthal plasma drift flow. A radial density profile of $n$ is described as a function of central radii $r_{c}$ .

Figure 1. (a) Time evolution of central X-ray radial intensities at the shot number of 200 400. Heating timings are also plotted in (a). Plug electron cyclotron heating (ECH) for radial shear formation was applied during 110.6–120.4 ms. (b) Central potential $\unicode[STIX]{x1D6F7}_{C}$ and (c) vorticity profiles $-W_{r}$ were plotted at 118.5 ms. Axially placed multichannel (two-dimensional) soft X-ray measurements are shown (d) during and (e)–(g) after the turn-off time of plug ECH ((d) 119.00 ms as well as (e) 122.50, (f) 124.61 and (g) 125.33 ms). The other main parameters were obtained as follows: the central line density $nl_{c}=3.6\times 10^{13}~\text{cm}^{-2},T_{i0}\sim 5~\text{keV}$ and $T_{e0}=0.5~\text{keV}$ with central (180 kW) and plug (360 kW) ECHs.

Experiments were carried out in a large mirror device of GAMMA 10. The detailed machine parameters in the employed standard operation were easily found in various references (Cho et al. Reference Cho, Kohagura, Numakura, Hirata, Hojo, Ichimura, Ishii, Itakura, Katanuma and Nakashima2001, Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a ,Reference Cho, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii, Islam and Itakura b ).

The presented paper by Smirnov (Reference Smirnov2016) was also characterized by $E_{r}$ shear effects of FRC plasmas on confinement improvement. Also, after the improvement, it was shown that plasma was drifting towards the wall without a rotation axis. These properties seemed to have similar essentials to those in figure 1(e–g) of mirror plasmas during loss of the shears (see below).

3 Experimental data and discussion

The presentation of a mirror at the APS in Orlando (Cho Reference Cho2007) was highlighted by the following characteristic properties: plasmas were basically produced and heated in ion temperatures of ${\sim}5~\text{keV}$ by ion-cyclotron heatings (ICH), initiated by magneto plasma dynamic guns. Externally controllable plasmas were formed by central electron cyclotron heating (central ECH) (figure 1) together with the other ECHs for shear flow formation (plug ECHs) (for more details, see Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a ,Reference Cho, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii, Islam and Itakura b ). It was, nevertheless, noted that preceding plug ECH was needed for stability for an electron temperature ( $T_{e}$ ) rise due to central ECH. Further, central ECH effects of the $T_{e}$ rise to 500 eV from an ultra-low-energy observable X-ray pulse height analyser (Kohagura et al. Reference Kohagura, Cho, Hirata, Yatsu, Tamano, Ogasawara, Yagishita, Sekitani and Maezawa1995) and microchannel plate X-ray tomography detectors (Hirata et al. Reference Hirata, Cho, Takahashi, Yamaguchi, Kondoh, Matsuda, Aoki, Tanaka, Maezawa and Miyoshi1992) were observed during the plug ECH injection.

In fact, when we injected the central ECH alone, plasmas strongly migrated and drifted towards a wall, and then crashed. An earlier time injection of the plug ECH (figure 1 a) has successfully formed high electron and ion temperature plasmas. In this article, analyses of the data for possibly wider uses of the common physics background were carried out.

In figure 1(a), the above-described sequence was performed. Central potential $\unicode[STIX]{x1D6F7}_{C}$ in figure 1(b) was measured with a radially scannable heavy-ion $(Au^{0})$ beam probe (HIBP) (Ishii et al. Reference Ishii, Kotoku, Segawa, Katanuma, Mase and Miyoshi1989). Gaussian shapes of central density and central potential profiles were again employed, as reported by previous various articles. When we utilized these values for the calculation of vorticity (see § 2), the curve of figure 1(c) was obtained. These profiles were nearly the same as those reported in previous articles (Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a ,Reference Cho, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii, Islam and Itakura b ).

The data in figure 1(a) and (c) showed the formation of a higher shear regime (core plasmas with $-W_{r}>1\times 10^{5}~\text{s}^{-1}$ in this experimental region) within $r_{c}<5~\text{cm}$ . On the contrary, the outer region of $r_{c}>5~\text{cm}$ was characterized as a lower vorticity one $(-W_{r}<1\times 10^{5}~\text{s}^{-1})$ . Here, the suffix $r$ denotes radially varied values of $W$ .

As we expected from figure 2 of our previous report (Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a ) (that is, turbulent core plasmas with smaller vorticity $(-W_{r}<1\times 10^{5}~\text{s}^{-1})$ were stabilized by higher vorticity formation $(-W_{r}>1\times 10^{5}~\text{s}^{-1})$ due to plug ECH), turbulent plasmas again clearly disappeared within $r_{c}\sim 5~\text{cm}$ having an appreciable amount of vorticity $(-W_{r}>1\times 10^{5}~\text{s}^{-1})$ as shown in figure 1(a) and (c).

After the turn-off time of shear flow formation (plug ECH), a striking characteristic property was highlighted. Lower shear plasmas again appeared with no ‘substantial plasma axis’ at $r_{c}=0$ , and no stable plasma conditions without a rotational axis were followed just after the turn-off time of $t=120.4~\text{ms}$ .

In fact, figure 1(e–g) clearly demonstrated the detailed structure of the unstable plasmas; that is, our developed multichannel X-ray detector placed axially $(/\!\,/\boldsymbol{B}_{0})$ using a combination of micro-channel plates (Hirata et al. Reference Hirata, Cho, Takahashi, Yamaguchi, Kondoh, Matsuda, Aoki, Tanaka, Maezawa and Miyoshi1992) and charge coupled devices in the central cell also demonstrated the complicated unstable plasma structures without a substantially symmetric axis. During the period with both ECHs, the axial structure of the soft X-ray detector signals was uniform in the core plasma regime with high vorticity (see figure 1 a–d)]. On the other hand, a strongly unstable plasma structure appeared together with a strong radial transport, despite the original magnetic lines of force existed (figure 1 e–g). This showed that unstable plasmas triggered a quick cross-field transport towards the plasma wall without a steady rotation axis.

From a more generalized physics viewpoint, these data and our previous reports (Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a , Reference Cho, Hirata and Pastukhov2006) totally and consistently indicated that an externally stable plasma control required a strong vorticity region together with a steady and substantial circulation axis.

In other words, core plasmas were guarded and maintained in terms of co-axially nested shear plasma formation using a slight loss of heated electrons into both end regions through loss cones for the radially sheared potential formation due to controlled ECH (Cho et al. Reference Cho, Yoshida, Kohagura, Hirata, Numakura, Higaki, Hojo, Ichimura, Ishii and Islam2005a ; Cho Reference Cho2007).

From this experimental evidence, FRC plasmas, for instance, also would have a possibility of a longer lifetime due to an externally controllable strong ECH; namely, co-axially nested shear plasma formation with a steady circulation axis. In addition, it would be of use in particular for high beta plasmas to employ off-axis ring-shaped flow plasmas due to ECH (Cho et al. Reference Cho, Hirata and Pastukhov2006, Reference Cho, Pastukhov, Horton, Numakura, Hirata, Kohagura, Chudin and Pratt2008). Such off-axis flow should be located between a separatrix surface and main FRC plasma for power saving and cost minimum vorticity stabilization.

For the experiments, it is noted from our experimental experiences that wall conditions with minimized recycling rate (i.e. clean walls) or only a little remaining gas near the wall were of importance for suppressing an additional uncontrollable plasma production. This contributed to produce a steady circulation axis axisymmetrically. A larger wall diameter or a higher pumping speed in the peripheral region (i.e. a large vacuum conductivity) should contribute much to the formation of (i) co-axially nested shear plasmas with the same individual rotational velocity as a function of $r_{c}$ around a substantial rotation axis or (ii) internal transport barrier formation (Cho et al. Reference Cho, Hirata and Pastukhov2006, Reference Cho, Pastukhov, Horton, Numakura, Hirata, Kohagura, Chudin and Pratt2008). Also, ECH fortunately minimized gas inlet as compared to neutral beam injections. Even if FRC plasmas had a rather short lifetime as compared to tokamaks, high quality stabilized plasmas would be of great use. Successive ‘pulsed’ formation of short but stable high quality and high beta plasmas, for example, might be of significant use similar to high quality laser plasmas. As a final note, a better performance of plug ECH was anticipated as compared to end plate biasing. Re-ionizing clouds of recombined ambient gas resulting from plasma outer flows into the end plate region would give possibilities of uncontrollable phenomena with high bias voltages. In relation to this, it is noteworthy that radial electric fields without end plates in rotating plasmas were in fact proposed for alpha channelling (Fetterman & Fisch Reference Fetterman and Fisch2008, Reference Fetterman and Fisch2010).

This predicted extension of mirror data to FRC experiments is, at this time, a candidate for possible improvements for plasma upgrades. However, an opportunity for such extension on the basis of plasma physics fundamentals would be important and essential. In other words, a similar external plasma control method having wider and common physics bases might contribute to various plasma devices more generally.

4 Summary

Co-axially nested shear plasma formation with a substantial and steady rotation axis has been demonstrated (figure 1) for the first time by the use of both plug and central ECHs. Each nested multi-shell-like structure had a good axisymmetry with the same individual rotational velocity circularly as a function of $r_{c}$ ; in other words, this showed that difference of the circular velocity (angular momentum) in each nested ‘ring-shaped shell’ guarded and co-axially wrapped up the core plasmas $(r_{c}<5~\text{cm})$ by themselves.

It was noteworthy that the highly improved central plasma heating due to central ECH with ICH could only be carried out in association with plug ECHs. This was interpreted in terms of high vorticity shear formation.

Its wider application or extension, for instance to FRC plasmas, would possibility help to solve one of presently unsolved problems through a similar essential physics viewpoint. At that time, either nested shear plasma formation or transport barrier formation in rather peripheral plasmas (Cho et al. Reference Cho, Hirata and Pastukhov2006, Reference Cho, Pastukhov, Horton, Numakura, Hirata, Kohagura, Chudin and Pratt2008) within the separatrix of FRC (Smirnov Reference Smirnov2016) would be a useful candidate for making stabilized upgrades of FRC or more generalized plasmas.