Helical magnetic field

Figure 23< 16 The tokamak design for magnetic containment of a fusion plasma. The donut-shaped chamber of the tokamak (photo, top schematic, bottom) contains the plasma within a helical magnetic field.

There is a contradiction between the low-shear limit of the Mercier criterion for a helical magnetic field and the closed--line criterion of a purely poloidal field. This apparent paradox was solved by Grad and Shafranov and Frolenkov who showed that the unstable spectrum either moves to high wave numbers where MHD theory does not apply, or that finite inertia decreases the growth rate to zero. The closed-line criterion predicts MHD stability under rather general conditions, in some cases even without shear and conducting walls. 

Helical undulators build on this principle by using two orthogonal magnetic field arrays [82, 83]. These permit transverse excursions in perpendicular x and y directions. If the arrays have a relative longitudinal shift, this introduces a phase to the induced perpendicular excursions and when the phase is 90° the electron trajectory can follow left- or right-handed corkscrew paths The emitted radiation is correspondingly right- or left-handed CPL. 

The transfer efficiencies (Fig. 12) for the a-helical and (3-strand substructures are 0.036 and 0.04, respectively. Therefore, calculations suggest that the HN(CO)CANH-TROSY experiment becomes superior to the HN(CO)CA-TROSY scheme, especially on (3-sheet substructures of high molecular weight proteins at the highest magnetic field currently available. 

The presence of a static magnetic field within a plasma affects microscopic particle motions and microscopic wave motions. The charged particles execute cyclotron motion and their trajectories are altered into helices along the field lines. The radius of the helix, or the Larmor radius, is given by the following ... 

Early experience also showed that the induced plasma current in a tokamak generates a magnetic field that loops die minor axis nf Ihe torus. The field lines form helices along the toroidal surface the plasma must cross the lines to escape. It does so through the cumulative action of many random displacements caused by interparticle collisions, tin effect diffusing across the field lines and out of the system). Thermal energy is transported by much the same process. 

When a current flows through a helical wire, a magnetic field is formed around that wire. This phenomenon is used to demonstrate superconductivity (fig. 11.4.14). 

The electric and magnetic fields are invariant under gauge transformations, 4 X(x) i—>A (x) + cM A(x). The effect of these transformations on the helicity has been treated by Marsh [49]. The variation of the magnetic helicity under a gauge transformation 8A = —VA is... 

The electric and magnetic fields are dual to one another and have the same properties in Maxwell theory in empty space. Given the divergenceless vector field B, we have defined the magnetic helicity as... 

Figure 11. (a) Helical distribution of linearly oscillating parallel electric and magnetic fields... 

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