Abstract
In this chapter we present the Hamiltonian formulation of the equations for magnetic field lines. We specifically consider the magnetic field corresponding the toroidal plasma configuration.
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Notes
- 1.
A diamagnetic current is created due to a circular motion of charged particles in an induced magnetic field. It produces a magnetic field which opposes the external magnetic field and thus the total magnetic field is reduced. Therefore a plasma possesses diamagnetic properties. Typically, the magnetic field due to a diamagnetic current is much smaller than the strong toroidal field \(B_0\).
- 2.
The magnetic flux \(\psi \) cannot be arbitrary small. According to the quantization rule, \(\oint p_zdz=h n\), (\(n=1,2,\dots \)), \(p_z= eA/c\) one has \(\psi = \varPhi _0 n\), where \(\varPhi _0=hc/e\) is a quant of magnetic flux [\(h\) is the Planck’s constant]. In fusion plasmas the magnetic flux is so large, that its discreteness does not play any role.
- 3.
Particularly, as will be discussed Chap. 11 the barriers to a particle transport caused by a small scale turbulent field may be formed near the low–order rational values of \(q\).
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Abdullaev, S. (2014). Hamiltonian Representation of Magnetic Field. In: Magnetic Stochasticity in Magnetically Confined Fusion Plasmas. Springer Series on Atomic, Optical, and Plasma Physics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-01890-4_1
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DOI: https://doi.org/10.1007/978-3-319-01890-4_1
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