Causes and precursors

A process, which violates the above-listed operational limits is referred to ascause. Causes are e. g. tile fragments, which fall into the plasma and perturb the equilibrium. Other examples are inaccuracies of external field coil positioning and irregularities in the coil shapes and current feeds to the coils. Due to deviations from axisymmetry, error fields in the toroidal field arise, which can - if large enough - interact with the fields of magnetic islands in the plasma. The interaction can lead to a retardation of the magnetic island rotation or even to a complete stop. The latter is denoted by ’mode locking’. A locked mode can also be produced actively by error field induced seed islands ([35] ... [38]). Figure III.1 shows a mode locking for a time duration of almost 10 ms, which ends up in a minor disruption. In the following, we will restrict the description of the multitude of precursors to an extent important for this work. This concerns the appearance of modes, of the MARFE and the minor disruption.

III.1. Causes and precursors 31

Magnetic modes are excited by exceeding one of the critical boundaries listed above.

As explained in Chapter II, magnetic modes arise in the vicinity of rational flux surfaces of a low q. The growth rate of m/n=2/1, 3/1 or 3/2 modes is often of non-linear char- acteristic and large modes can initiate a rapid thermal energy expulsion in the form of a minor or a major disruption. The occurrence of a low-m, low-n magnetic mode is a disruption precursor. Modes can be detected and techniques are studied, in which ECRH heating is applied for controlling the mode growth [68].

Figure III.1 shows an occurrence of several modes in the low-qdischarge2 _{#24413. As a}

precursor for the first two minor disruptions, a changing mode activity is identified. In the first one, the mode amplitude grows, which could have caused an overlap of neighbouring modes. Stochastic variations of the pathways of magnetic field lines could possibly arise in such a condition, which leads to an enhanced radial transport and a loss of confinement. The second minor disruption was signalised by the slowly rotating m/n = 3/1 mode between 0 and 16 ms and its locking marked by the green cursor.

Mode locking is based on resistive MHD [39], [40]. The locked modes are resistive

tearing modes in the vicinity of the rational surface q = m/n [47]. A mode rotates toroidally due to a torque caused by superimposed effects such as diamagnetism or e. g. NBI momentum input. If the mode results in island formation and the island is of sufficient width to induce significant eddy currents in the surrounding conductors, an opposite torque retroacts on the rotation and reduces the plasma rotation [41]. This is a normal condition and applies generally. However, if the error field matches the mode in a way that it reduces the plasma rotation to a sufficient extent, an abrupt locking could occur. When the mode is locked, it ultimately grows and reduces the confinement due to the flattened pressure inside and the short-circuited internal temperature, which results in an efficient radial transport. An example for mode locking is presented in Figure III.1.

The uncontrolled MARFE, is known to be a precursor for density limit disruption

[96]. It is a cold radiation condensation instability3 _{appearing when the density limit in}

the edge is approached [50]. The threshold density scales linearly with the plasma current

Ip . The MARFE appears as a toroidal structure. It is poloidally localised partly in the

SOL and - in small parts - also within the confined plasma region [43]. The radiated energy is related to the temperature Te, the impurity mix and the radiation potential

of the relevant impurities. As presented in the previous chapter, Figure II.4 shows the radiation potential versus Te for several elements. The functions presented on the right

have a pronounced maximum. In regions with a negative derivative, a local temperature

2

The purpose of the discharge (studies on X3-mode heating) is explained in [95]. The ECRH system is overviewed in [94].

3

E_th

i l current hump due to dip of internal plasma inductance

n B d dt I_p thermal energy plasma current

Mirnov coils measure

current quench

minor disruption

minor disruption

in a cooled plasma resistivity riseor final thermal quench

magnetic mode

rotation plasma column moves

confinement re−established θ minor disruption (ms) t* (a. u.)

(a. u.) yellow−magenta = poloidally oppositely located

yellow−blue = toroidally oppositely located

mode locking

Figure III.1: Series of minor disruptions and mode locking (discharge #24413). Find the signal

labels as attachments to the plots. The x₋axis is zeroed at t = 2.8932 s for making the time

scale more feasible. Magnetic coils measure the change of the poloidal magnetic field in the vessel wall vicinity on the midplane [93].

decrease would lead to an increase of radiation losses - this corresponds to an instable condition. If the radiation loss cannot be compensated by heat conduction [60], the local volume becomes thermally unstable, grows or starts to move [49]. We call this condition anuncontrolled MARFE regimein this work. The cause of such a regime is an insufficient energy flux across the plasma boundary into the MARFE volume. If the other extremum is the case, namely a too high energy flux into the edge, then, the MARFE flushes out [43] and impurities are redistributed. A controlled MARFE regime establishes in cases of a well-balanced input/output condition meaning the core must be hot enough for providing the energy flux for stabilising the MARFE in the edge.

Minor disruptions are possible precursors of a major disruption. A minor disruption

shows features comparable to the thermal quench. It differs from the thermal quench in the regard of the Eth expulsion: A minor disruption only removes a fraction - a thermal

quench expels the full magnitude of Eth. A minor disruption in fact modifies density,

pressure and current profiles but does not affect the plasma in such a way that it leads to a full expulsion ofEth and a subsequent current quenching. The discharge thus continues.

In Figure III.1, a series of minor disruptions removes successively the thermal energy contentEthfrom the plasma with intermediateEthrises. After the third minor disruption,

however, the plasma is cooled such that the current quenches. This quench is the major disruption.

A minor disruption is a precursor to a major disruption, because it could affect the density, pressure and current profiles such that boundaries are exceeded.

III.1. Causes and precursors 33