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When a rather cold electron bunch is transported during laser bubbleacceleration in a strongly focusing plasma channel with typical forces of 100GeV/m, it will form partially ordered long electron cylinders due to therelativistically longitudinal reduced repulsion between electrons, resulting ina long-range pair correlation function, when reaching energies in thelaboratory above 0.5 GeV. During Compton back-scattering with a second laser,injected opposite to the electron bunch, the electron bunch will be furthermodulated with micro bunches and due to its ordered structure will reflectcoherently, M\"ossbauer-like, resulting in a \gamma free electron laser(\gamma-FEL). Increasing the relativistic \gamma factor, the quantal regimebecomes more dominant. We discuss the scaling laws with \gamma.

A Quantal, Partially Ordered Electron Structure as a Basis for a \gamma Free Electron Laser (\gamma-FEL)