ORIGINAL RESEARCH Scaling Laws of Bulk Plasma Parameters for a 1-D Flow through a Capillary with Extended Converging–Diverging Nozzle for Simulated Expansion into Fusion Reactor Chamber Rudrodip Majumdar • John G. Gilligan • A. Leigh Winfrey • Mohamed A. Bourham Ó Springer Science+Business Media New York 2015 Abstract A capillary-extended converging–diverging transition region was previously proposed to allow for the flow and expansion of plasma into a large volume simulating aerosol expansion and particle transport in the active volume of a fusion reactor. It has been shown that the pulsed electrothermal plasma source was adequate for the simulation, and the expansion into the chamber is at steady conditions for the main plasma parameters indicat- ing a uniform expansion of the aerosol following a dis- ruption event. These parameters are the bulk temperature, density, pressure, plasma bulk velocity and Mach number for the same system geometrical configuration. Scaling laws in 1-D for bulk plasma parameters have been devel- oped for ranges of axial length traversed by the flow to predict these parameters along the axis of the expansion chamber. Keywords Plasma flow  Fusion particle expansion  Electrothermal plasma scaling laws Introduction Expansion of aerosol particulates into the vacuum chamber of a fusion reactor following a hard disruption event was previously investigated using a supersonic nozzle on the exit of an electrothermal capillary discharge to allow for the transition between the source and the chamber’s large volume [1]. A schematic of the capillary discharge with the attached expansion is shown in Fig. 1 in which a subsonic to supersonic transition region is inserted between the electrothermal source and the expansion chamber [1]. The capillary source simulates hard disruption events by depositing transient radiant high heat flux onto the inner liner of the capillary, which in turn generates particulates from wall evaporation [2, 3]. The particulates form a plasma jet, which moves towards the capillary exit at high speed and high pressure. The capillary serves as a source term simulating surface erosion of the divertor of a tokamak fu- sion reactor under hard disruption-like conditions [4, 5]. The plasma jet expands into the vacuum vessel, which is simulated herein by the expansion large chamber. The noz- zle, converging–diverging, is a method to allow for the computational transition between the capillary exit and the entry of the expansion chamber [1]. The capillary has an inner diameter of 4.0 mm diameter and 12 cm in length with 3.0 cm occupied by the discharge cathode. The discharge time is in the range of 100–200 ls and can be extended to few milliseconds. The produced plasma jet has typical tem- perature of up to 5 eV, an exit peak pressure of up to 400 MPa and imparts a radiant heat flux up to 60 GW/m 2 [3]. In the previous work, it has been shown that the Mach number at the diverging exit drops from 21 to 0.7 after suffering from multiple shocks in the large expansion volume, and that the plasma parameters are almost constant along the axis of the simulated expansion chamber [1]. It R. Majumdar  J. G. Gilligan  M. A. Bourham (&) Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695-7909, USA e-mail: bourham@ncsu.edu R. Majumdar e-mail: rmajumd@ncsu.edu J. G. Gilligan e-mail: gilligan@ncsu.edu; john_gilligan@ncsu.edu A. L. Winfrey Department of Material Science and Engineering, University of Florida, Gainesville, FA 32611-6400, USA e-mail: winfrey@mse.efl.edu 123 J Fusion Energ DOI 10.1007/s10894-015-9899-2