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Bicircular twisted Laguerre-Gaussian beams possess a definite torus knotangular momentum (TKAM) as a new form of angular momentum. TKAM is conserved innonlinear atomic processes such as high harmonic generation and can beclassified by a time delay parameter $\tau$ and a coordination parameter$\gamma$. These parameters are defined by the respective projected orbitalangular momentum and the energy of the two superimposed Laguerre-Gaussianbeams. We derive a consistent geometric method to determine $\tau$ and $\gamma$from the driving beam as well as from the high harmonic radiation. This methodrelates both invariance parameters ($\tau$ and $\gamma$) to the emitted highharmonic radiation. Therefore, $\tau$ and $\gamma$ can be read off of twodifferent torus knots. These knots can be constructed from the spatio-temporalevolution of the electric field of the respective high harmonic radiation orthe driving beam. We demonstrate the classification of the invarianceparameters for a planar atomic gas target irradiated by bicircularLaguerre-Gaussian beams explicitly. Furthermore, we demonstrate that therespective torus knots determined by $\tau$ and $\gamma$ can be mapped ontoeach other within minor modifications. This geometric method yields a differentway to interpret the invariance parameters $\tau$ and $\gamma$ as well as theirunderlying relation compared to a purely formal derivation. The investigationspresented in this work are in good agreement with previous findings and provideinsight into the dynamical symmetry of TKAM in the context of high harmonicgeneration induced by bicircular twisted Laguerre-Gaussian beams.

Torus Knot Angular Momentum in Twisted Attosecond Pulses from High Harmonic Generation