The application of laser pulses with psec or shorter duration enables nonthermal efficient ultrahigh acceleration of plasma blocks with homogeneous high ion energies exceeding ion current densities of $10^{12}~\text{A}~\text{cm}^{-2}$. The effects of ultrahigh acceleration of plasma blocks with high energy proton beams are proposed for muon production in a compact magnetic fusion device. The proposed new scheme consists of an ignition fusion spark by muon catalyzed fusion ($\unicode[STIX]{x03BC}$CF) in a small mirror-like configuration where low temperature D–T plasma is trapped for a duration of $1~\unicode[STIX]{x03BC}\text{s}$. This initial fusion spark produces sufficient alpha heating in order to initiate the fusion process in the main device. The use of a multi-fluid global particle and energy balance code allows us to follow the temporal evolution of the reaction rate of the fusion process in the device. Recent progress on the ICAN and IZEST projects for high efficient high power and high repetition rate laser systems allows development of the proposed device for clean energy production. With the proposed approaches, experiments on fusion nuclear reactions and $\unicode[STIX]{x03BC}$CF process can be performed in magnetized plasmas in existing kJ$/$PW laser facilities as the GEKKO-LFEX, the PETAL and the ORION or in the near future laser facilities as the ELI-NP Romanian pillar.