The role of stochasticity in sawtooth oscillations

Lichtenberg, A. J.; Itoh, K.; Itoh, Sanae I.; Fukuyama, A.

doi:10.1088/0029-5515/32/3/i12

Cited by 111 publications

(107 citation statements)

References 27 publications

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“…The derived diffusion coefficients can be transformed into the electron thermal diffusivity e χ by means of the expression [7]:…”

Section: Sawtooth Crashmentioning

confidence: 99%

Diffusion in a stochastic magnetic field in ASDEX Upgrade

Dumbrājs¹,

Igochine²,

Zohm³

2008

Nucl. Fusion

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Heat diffusion coefficients in a stochastic magnetic field are determined in the case of frequently interrupted regime of neoclassical tearing modes and of incomplete sawtooth reconnection in ASDEX Upgrade tokamak. Here the experimentally measured perturbations and profiles are used and the mapping technique is applied. With the derived diffusion coefficients the nonstationary diffusion equation is solved, making it possible to study time evolution of fast MHD phenomena in ASDEX Upgrade. The proposed phenomenological approach relies heavily on experimental information and requires very moderate computing resources.

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“…The derived diffusion coefficients can be transformed into the electron thermal diffusivity e χ by means of the expression [7]:…”

Section: Sawtooth Crashmentioning

confidence: 99%

Diffusion in a stochastic magnetic field in ASDEX Upgrade

Dumbrājs¹,

Igochine²,

Zohm³

2008

Nucl. Fusion

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“…Thus, such theories cannot describe sawtooth events observed in ASDEX Upgrade. In this paper, we employ the stochasticity hypothesis which was proposed to explain the sawtooth phenomenon without a full reconnection [9,10] assuming the interaction of the (1,1) mode with other periodicities and utilizing on the Hamiltonian formalism. The work consists of five sections.…”

Section: Introductionmentioning

confidence: 99%

Stochastic sawtooth reconnection in ASDEX Upgrade

et al. 2006

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In this paper we investigate non-complete Sawtooth reconnection in ASDEX Upgrade tokamak.Such reconnection phenomena are associated with internal m/n=1/1 kink mode which does not vanish after the crash phase (as would be the case for complete reconnection). It is shown that this sawtooth can not be fully described by pure m/n=1/1 mode and that higher harmonics play an important role during the Sawtooth crash phase. We employ the Hamiltonian formalism and reconstructed perturbations to model incomplete Sawtooth reconnection. It is demonstrated that stochastization appears due to excitation of low-order resonances which are present in the corresponding q-profiles inside the 1 q = surface which reflects the key role of the 0 q value.Depending on this value two completely different situations are possible for one and the same mode perturbations: (i) the resonant surfaces are present in q-profile leading to stochasticity and sawtooth crash ( 0 0.7 0.1 q ≈ ± ); (ii) the resonant surfaces are not present which means no stochasticity in the system and no crash event ( 0 0.9 0.05 q ≈ ± ). Accordingly central safety factor value is always less than unity in case of non-complete sawtooth reconnection. Our investigations show that stochastic model agrees well with experimental observations and can be proposed as a promising candidate for explanation of the sawtooth reconnection.

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“…However, the triggering of a secondary instability [14][15][16] by the strong pressure gradient arising from the reconnection process, can provide a simultaneous explanation of these phenomena. Recent advances in imaging electron temperature fluctuations with high temporal and spatial resolution [18] suggest that the global stochasticity of the magnetic field [13] is not the dominant crash mechanism since the heat transport exhibits well organised, collective behaviour. Whilst previous experimental data has given great insight into the phenomenology of the crash [7,18,19], it had insufficient radial resolution to provide either validation or vitiation of the concept of triggering of secondary instabilities [8,15,16], and theoretical or numerical comparison has been stifled by this.…”

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confidence: 99%

Magnetic Reconnection Triggering Magnetohydrodynamic Instabilities during a Sawtooth Crash in a Tokamak Plasma

et al. 2010

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High resolution Thomson scattering measurements with sub-centimetre radial resolution have been made during a sawtooth crash in a fusion plasma in MAST. As magnetic reconnection occurs, a growing magnetic island induces an increase in the temperature gradient at the island boundary layer, before a very rapid collapse of the core temperature. The increase in the local temperature gradient is sufficient to make the plasma core unstable to ideal magnetohydrodynamic instabilities, thought to be responsible for the rapidity of the collapse.PACS numbers: 52.55Fa, 52.35PyMagnetic reconnection is the phenomenon of the breaking and rejoining of magnetic field lines in a plasma. Examples of this process are solar flares in astrophysical plasmas [1,2] and the sawtooth instability in tokamak plasmas [3,4]. Whilst the sawtooth instability was first observed in 1974 [5], the process by which this periodic collapse of the core plasma temperature occurs is still only partially understood. Detailed diagnosis of the sawtooth crash has shown that the temperature profile is initially essentially axisymmetric, but is then deformed by a helical instability before a very rapid temperature collapse re-establishes an axisymmetric profile with a lower value at the magnetic axis [6,7].Tokamak plasmas are susceptible to sawtooth oscillations when the safety factor, q = rB φ /RB θ is less than unity [8], where r, R are the minor and major radii and B φ , B θ are the toroidal and poloidal magnetic fields. The helical perturbation which arises during the crash has an m = n = 1 structure, where m, n are the poloidal and toroidal periodicity of the wave. The first explanation of the periodic temperature collapses was proposed by Kadomtsev [3], who showed that in the nonlinear regime of the m = 1 mode, reconnection occurs at the separatrix on the characteristic Sweet-Parker timescale [1,2] 2 /ηc 2 is the resistive diffusion time, ρ is the mass density, η is the plasma resistivity and S = τ R /τ A is the Lundquist number. This timescale is up to two orders of magnitude too large to explain crash times in large modern-day tokamaks, where τ crash ∼ 20 − 100µs, whereas τ K = 2 − 10ms.The three principal observations which any theory must explain are (i) the rapidity of the temperature collapse, (ii) the sudden onset of the collapse and (iii) the incomplete relaxation of the current profile whereby q remains below unity whilst the temperature profile relaxes completely. The onset of the crash represents a theoretical challenge, since the incremental change in the safety factor which governs the stability of the m = n = 1 mode is unacceptably small to explain the rapid onset. Many alternative crash models have since been proposed, including resistive two-fluid MHD [9], collisionless kinetic effects [10,11], accelerated complete reconnection due to nonlinear collisionless effects [12], magnetic stochastization leading to enhanced perpendicular transport [13] and triggering of secondary instabilities [14][15][16]. Each of these models has had proponents...

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The role of stochasticity in sawtooth oscillations

Cited by 111 publications

References 27 publications

Diffusion in a stochastic magnetic field in ASDEX Upgrade

Diffusion in a stochastic magnetic field in ASDEX Upgrade

Stochastic sawtooth reconnection in ASDEX Upgrade

Magnetic Reconnection Triggering Magnetohydrodynamic Instabilities during a Sawtooth Crash in a Tokamak Plasma

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