Finite-Pressure-Gradient Influences on Ideal Spheromak Equilibrium

Hart, G. W.; Chin-Fatt, C.; DeSilva, A.W.; Goldenbaum, G. C.; Heß, R.; Shaw, Robert S.

doi:10.1103/physrevlett.51.1558

Cited by 29 publications

(19 citation statements)

References 11 publications

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“…The most interesting part of this spheromak solution is the nonconstant profile for J · B/B 2 plotted against normalized distance from the magnetic axis. This profile shows peaks outside the magnetic axis, and this feature is qualitatively closer to the experimentally observed profile reported by Hart et al [Hart et al, 1983].…”

Section: Single Fluid Mdr Based Modelsupporting

confidence: 91%

Minimum dissipative relaxed states applied to laboratory and space plasmas

Dasgupta¹,

Shaikh²,

Hu³

et al. 2009

J. Plasma Phys.

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Abstract. The usual theory of plasma relaxation, based on the selective decay of magnetic energy over the (global) magnetic helicity, predicts a force-free state for a plasma. Such a force-free state is inadequate to describe most realistic plasma systems occurring in laboratory and space plasmas as it produces a zero pressure gradient and cannot couple magnetic fields with flow. A different theory of relaxation has been proposed by many authors, based on a well-known principle of irreversible thermodynamics, the principle of minimum entropy production rate which is equivalent to the minimum dissipation rate (MDR) of energy. We demonstrate the applicability of minimum dissipative relaxed states to various self-organized systems of magnetically confined plasma in the laboratory and in the astrophysical context. Such relaxed states are shown to produce a number of basic characteristics of laboratory plasma confinement systems and solar arcade structure.

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Section: Single Fluid Mdr Based Modelsupporting

confidence: 91%

Minimum dissipative relaxed states applied to laboratory and space plasmas

Dasgupta¹,

Shaikh²,

Hu³

et al. 2009

J. Plasma Phys.

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“…In contrast, spheromaks often have p values above those predicted. 9 ' 10 In this Letter, strong evidence for a pressure-driven instability in CTX 11 spheromaks is presented. The instability leads to a distinct event in the discharge which can be analyzed in detail.…”

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confidence: 87%

Evidence for a Pressure-Driven Instability in the CTX Spheromak

et al. 1988

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Recent improvements in the operation of the CTX spheromak device have produced discharges containing evidence for a pressure-driven instability. The instability leads to a distinct event in the discharge, which can be studied in detail. Data are presented which reasonably discount Taylor relaxation of the current profile as the cause of the event. The critical value of the normalized pressure gradient has been measured and is compared with the Mercier limit.PACS numbers: 52.55.Hc, 52.35.Py A spheromak is a toroidal magnetic configuration with large toroidal and poloidal plasma currents which generate most of the internal magnetic field. This configuration is attractive for a fusion reactor because it is compact, has a high level of Ohmic heating power, and thus, may not require auxiliary heating (such as neutral beam or rf injection), and has a high engineering p (pcng&P/Blaw). However, the theoretically predicted internal p (p yo \ocP/(B 2 \ 0 \) calculated with the Mercier criterion is small, ranging from « 0.2% for the "classical" spheromak 1 to (1-2)% for nonspherical cross sections, 1 " 3 to ?£7% for the spheromaks with current holes. 2 " 4 In fact, many other toroidal magnetic configurations have low predicted p limits. Tokamaks are theoretically limited by the ballooning criterion 5 to ;S(5-10)%, and reversed field pinch equilibria stable to current-driven resistive tearing modes have a predicted p limit 6 of « 20%. The experimental significance of predicted p limits is often unclear, since other effects might limit plasma performance. If the p limits could be reached, the expected plasma behavior is often unknown. Tokamaks historically have had difficulty reaching the predicted p limit, 5 but recently large tokamaks have been used to explore plasma conditions at reactor relevant p values. The highest values obtained are empirically found to follow a scaling law of the form Pmax^3I/aB On %, MA, m, and T) 7,8 ; however, this can be consistent with either ballooning mode or kink mode limits. 7 In addition, operation at this p limit is found to be disruptive 7 in some cases and in other cases a degradation of energy confinement without disruption is observed. 8 Reversed field pinches normally operate 6 with roughly constant p («10%), indicating an empirical limit, but the value is less than the predicted value, which does not include the localized resistive interchange mode (sometimes called the "g mode"). In contrast, spheromaks often have p values above those predicted. 9 ' 10 In this Letter, strong evidence for a pressure-driven instability in CTX 11 spheromaks is presented. The instability leads to a distinct event in the discharge which can be analyzed in detail. It is found that when a particular threshold value in the pressure gradient is exceeded, internal plasma is expelled toward the wall in 10-20 jus. The resulting temperature and density profiles are both hollow (about the magnetic axis), strongly indicating a magnetic flux interchange. These hollow profiles are short lived, and evolve back to mod...

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“…These analytic solutions should be useful for extending interchange stability calculations [21][22][23] of spheromaks to finite ␤ and also for suggesting optimum wall shapes. Figure 2 gives plots of q wall , q axis , ␤, and h/r 0 as functions of ␥r 0 and kr 0 ; the locus of solutions with ␥r 0 ϭx 01 ϭ2.405 are the ␤ϭ0, force-free solutions.…”

Section: B Safety Factormentioning

confidence: 99%

Generalization of cylindrical spheromak solution to finite beta and large reversed shear

Bellan

2002

Physics of Plasmas

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The well-known analytic solution for a spheromak in a cylindrical flux conserver is generalized to the situation of finite ␤ with the shape of the flux conserver now being a dependent quantity. Analytic expressions are found for the poloidal flux surfaces, beta, the safety factors at both the magnetic axis and the wall, and the wall profile. A large reversed shear ͑i.e., ratio of safety factor on magnetic axis to safety factor at the wall͒ can be obtained at finite beta. This feature may be important because reversed shear in the core of tokamaks has been shown to permit stable operation at high ␤.

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Finite-Pressure-Gradient Influences on Ideal Spheromak Equilibrium

Cited by 29 publications

References 11 publications

Minimum dissipative relaxed states applied to laboratory and space plasmas

Minimum dissipative relaxed states applied to laboratory and space plasmas

Evidence for a Pressure-Driven Instability in the CTX Spheromak

Generalization of cylindrical spheromak solution to finite beta and large reversed shear

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