Abstract
A model describing the evolution of the average plasma temperature inside a discharge capillary device including Ohmic heating, heat loss to the capillary wall, and ionization and recombination effects is developed. Key to this approach is an analytic quasistatic description of the radial temperature variation which, under local thermal equilibrium conditions, allows the radial behavior of both the plasma temperature and the electron density to be specified directly from the average temperature evolution. In this way, the standard set of coupled partial differential equations for magnetohydrodynamic (MHD) simulations is replaced by a single ordinary differential equation, with a corresponding gain in simplicity and computational efficiency. The on-axis plasma temperature and electron density calculations are benchmarked against existing one-dimensional MHD simulations for hydrogen plasmas under a range of discharge conditions and initial gas pressures, and good agreement is demonstrated. The success of this simple model indicates that it can serve as a quick and easy tool for evaluating the plasma conditions in discharge capillary devices, particularly for computationally expensive applications such as simulating long-term plasma evolution, performing detailed input parameter scans, or for optimization using machine-learning techniques.
Highlights
It has been shown that the on-axis plasma temperature and electron density calculated in existing full 1D MHD simulations, which solve a complex system of coupled partial differential equations, can be remarkably well reproduced by the quasistatic uniform-energy-source temperature (QUEST) method, which solves a single, simplified ordinary differential equation for the average plasma temperature evolution
The key to the QUEST method is in the assumptions made about the radial temperature behavior, which specify the remaining plasma properties under local thermal equilibrium conditions
The approach followed here is to split the temporal evolution of the plasma into a “uniform regime,” where the plasma temperature is radially uniform, and a “quasistatic regime” where the plasma temperature has a nonuniform but analytic representation under quasistatic conditions
Summary
The ability to characterize and control the plasma conditions within gas-filled capillary discharge devices, including plasma wakefield acceleration sources [1,2,3,4,5,6,7], plasma waveguides [8,9,10,11,12], and active plasma lenses [13,14,15,16,17,18,19], is critical to the development and optimization of next-generation compact particle accelerator technologies [20]. Reduced geometry and simple equilibrium models have been shown to capture the essential physics for many applications [8,11,16] These investigations have demonstrated that stable quasistatic conditions are reached during the discharge that can be well described by reduced MHD models. The balance between Ohmic heating and boundary heat loss results in distinctive temperature and electron density profiles, which can be exploited for guiding high intensity laser pulses [8] and mitigated for active plasma lensing applications [17]. The plasma dynamics are captured via a model of the average energy evolution, i.e., a single ordinary differential equation. This is achieved through assumptions about the radial variation of the plasma properties based on quasistatic conditions.
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