**5. References**

130 Topics in Magnetohydrodynamics

In the MRX device, the stability of oblate FRC plasma was investigated. The plasma parameters are electron density of 0.5 - 2 x 1020 m-3, ion temperature of ~18 eV, *B*z of 300 - 200 G, *E* of 0.65 - 0.35, *s* of 1-3, and *s E* of 2-5 (Gerhardt et al., 2006). Without a passive stabilizer (a hollow conducting center conductor), tilt and shift instability (*n* = 1 mode of Fig. 10 (a) and (b)) often appeared. The tilt mode limits the plasma lifetime. The tilt instability can be mitigated by either including a passive stabilizing conductor or forming highly oblate plasmas with a strong mirror field. Without the center column, the growth of the shift mode is reduced, apparently by the large magnetic fields on the outboard side of device. Large perturbations (*n* = 2 and 3) may still remain after passive stabilization is applied ((b) and (c) of Fig. 10 (a)). These perturbations have the characteristics of co-interchange modes, which have never been observed in conventional oblate FRCs. Such modes cause the early termination of the oblate FRC shape. These co-interchange modes can be stabilized in oblate plasma with a high mirror ratio, and this produces an FRC with maximum configuration

In Table 4, the MHD stability properties of both prolate and oblate FRCs are summarized (Yamada et al., 2007). In oblate FRC plasma, the global mode (*n* = 1 external tilt and shift mode, co-interchange mode) is unstable. But these modes can be stabilized by employing a close-fitting conducting shell or shaping with a strong external magnetic field. In prolate plasma, the internal tilt mode and co-interchange mode are MHD-unstable. However, these can be stabilized by nonlinear effects, such as FLR, rotation and sheared flow. It is difficult to observe these modes clearly in the experiments. The most destructive rotational mode (*n* = 2), and wobble (*n* = 1) mode, are almost always observable in experiments. Active stabilization methods without degradation of confinement, such as CHI, need to be

> MHD unstable, stabilized by FLR, rotation and nonlinear effects for S\*<20, E 5.

> > FLR

compressional effects

MHD unstable, stabilized by quadrupole field, RMF and conducting shell

Co-interchange, n>1 MHD unstable, stabilized by

Interchange, n>1 MHD unstable, stabilized by

Table 4. Stability properties of prolate and oblate FRCs

Shift, n=1 MHD stable MHD unstable, stabilized by

**Prolate [E>1] Oblate [E<1]** 

MHD Stable

conducting shell

MHD unstable, stabilized by NBI + conducting shell

MHD unstable, stabilized by compressional effects

MHD unstable, stabilized by quadrupole field, RMF and conducting shell

**3.2 MHD behavior and stability of oblate FRCs** 

lifetime.

**4. Summary** 

developed.

Internal Tilt, n=1

Rotational, n=2

External Tilt and Radial


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38

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**0**

**6**

Ivan Zhelyazkov

*Bulgaria*

*Faculty of Physics, Sofia University*

**Review of the Magnetohydrodynamic Waves and**

One of the most enduring mysteries in solar physics is why the Sun's outer atmosphere, or corona, is millions of kelvins hotter than its surface. Among suggested theories for coronal heating is one that considers the role of spicules – narrow jets of plasma shooting up from just above the Sun's surface – in that process (Athay & Holzer, 1982; Athay, 2000). For decades, it was thought that spicules might be sending heat into the corona. However, following observational research in the 1980s, it was found that spicule plasma did not reach coronal temperatures, and so this line of study largely fell out of vogue. Kukhianidze et al. (Kukhianidze et al., 2006) were first to report the observation of kink waves in solar spicules – the wavelength was found to be ∼3500 km, and the period of waves has been estimated to be in the range of 35–70 s. The authors argue that these waves may carry photospheric energy into the corona and therefore can be of importance in coronal heating. Zaqarashvili et al. (Zaqarashvili et al., 2007) analyzed consecutive height series of H*α* spectra in solar limb spicules at the heights of 3800–8700 km above the photosphere and detected Doppler-shift oscillations with periods of 20–25 and 75–110 s. According to authors, the oscillations can be caused by waves' propagation in thin magnetic flux tubes anchored in the photosphere. Moreover, observed waves can be used as a tool for spicule seismology, and the magnetic filed induction in spicules at the height of ∼6000 km above the photosphere is estimated as 12–15 G. De Pontieu et al. (De Pontieu et al., 2007) identified a new class of spicules (see Fig. 1) that moved much faster and were shorter lived than the traditional spicules, which have speeds of between 20 and 40 km s−<sup>1</sup> and lifespans of 3 to 7 minutes. These Type II spicules, observed in Ca II 854.2 nm and H*α* lines (Sterling et al., 2010), are much more dynamic: they form rapidly (in ∼10 s), are very thin (200 km wide), have lifetimes of 10 to 150 s (at any one height), and shoot upwards at high speeds, often in excess of 100–150 km s−1, before disappearing. The rapid disappearance of these jets had suggested that the plasma they carried might get very hot, but direct observational evidence of this process was missing. Both types of spicules are observed to carry Alfvén waves with significant amplitudes of order 20 km s−1. In a recent paper, De Pontieu et al. (De Pontieu et al., 2011) used new observations from the Atmospheric Imaging Assembly on NASA's recently launched *Solar Dynamics Observatory* and its Focal Plane Package for the Solar Optical Telescope (SOT) on the Japanese *Hinode* satellite. Their observations reveal "a ubiquitous coronal mass supply in which chromospheric plasma in fountainlike jets or spicules (see Fig. 2) is accelerated upward into the corona, with much of the plasma heated to temperatures between ∼0.02 and 0.1 million kelvin (MK) and a small but sufficient fraction to temperatures above 1 MK. These observations provide constraints

**1. Introduction**

**Their Stability in Solar Spicules and X-Ray Jets**

Yamada, M., et al., (2007), A Self-Organized Plasma with Induction, Reconnection, and Injection Techniques: the SPIRT Concept for Field Reversed Configuration Research, *Plasma and Fusion Research*, Vol. 2, 004, pp. 1-14
