However, a large amount of energy can be stored in and released from the surrounding field structure but only if either or both currents, I, take on lower values. This is easily demonstrated in the example in Fig. 2, which is given in the following. The total energy that has been delivered to an electrical element, by time T0 is given by:
[latex]W(t_{0})=\int_{-\infty }^{t_{0}}v(t)i(t)dt.[/latex] (6)
For the case of the flux-linked conductors in the example, i(t) = 2I, and v(t) is the voltage drop across a unit length of the conductor in the direction of i(t). Faraday’s law indicates that;
[latex]v(t)=\frac{d\phi(t)}{dt}[/latex] (7)
where Phi ([latex]\phi[/latex]) is the total magnetic flux that links the conductors. Thus, the energy that is stored in the magnetic field that surrounds the conductors at time t0 is given by;
[latex]W(t_{0})=\int_{-\infty}^{t_{0}}\frac{d\phi}{dt}i(t)dt=\int_{\phi(-\infty)}^{\phi(t_{v})}id\phi[/latex] (8)
Where the total magnetic flux depends on the current’s amplitude, i.e.,
[latex]\phi(t)=Li(t)[/latex] (9)
The constant of proportionality L is called the inductance, which may be a constant or a function of φ. When a current flows in large regions, this single inductance element L should be replaced by a transmission line, and the situation is then more accurately (but less intuitively) described by partial differential equations [1]. Equations (6)–(9) demonstrate the basic principle that the total energy that is stored magnetically in the infinite volume surrounding the conductors completely depends on the current. That is, using (9), (8) may be written as an integral in terms of only the current. The total energy that will be released from this volume over any time interval is thus clearly a function of the change in current amplitude over that interval.
If these twin currents are disrupted (e.g., by an exploding DL in their path), the field will quickly collapse and liberate all of the stored magnetic energy that is given by (8).
Investigators who prefer to avoid explicit mention of electric current as a primary cause of cosmic energy releases fall back on magnetic reconnection as an explanation. The crucial difference between the two explanations is the question of which quantity (time-varying electric current or moving magnetic “lines”) causes energy release from the magnetized plasma.
