Abstract
It is well known that the magnetic helicity is not a single invariant in ideal magnetohydrodynamics. We study the problem of whether the exponent -1.7 of the slope of the turbulent spectrum of magnetic energy can be explained. An affirmative answer is obtained. The answer is based on the use of the M-invariant (numerical measure of knottedness of magnetic lines), which admits asymptotic and ergodic properties. On the present paper a foundation, which is required to construct such an invariant M5 is proposed. We shall prove a combinatorial formula for the M5 invariant and present a calculation of its dimension.
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