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We often need to suggest a value of current in a coil of gauss-gun i ≈ (E·v)/(U·l) The formula is precise when its components are constant. Thus, it works best for middle and last coils of multistage accelerator fed by common capacitor, where velocity and voltage change negligbly.
It is sometimes necessary to determine a moment of time when curent in a coil achieves its maximal value. This moment is described by the next complicated equation (as it is shown
where is capacitive constant of the circiut, inductive constant, damping factor, R, C, L - resistance, capacitance and inductance, respectively, arth - hyperbolic arctangent ( Fortunately, this formula can be substantially simplified for strongly overdamped systems, where Alas, decomposing the equation above to Taylor series and neglecting the second-order terms, we have just:
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