Thermal design of cathode with barium thermo-emitter

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


Sinitsin A. P.1*, Parakhin G. A.1*, Rumyantsev А. V.2**

1. Experimental Design Bureau “Fakel”, 181, Moskovsky av, Kaliningrad, 236001, Russia
2. Immanuel Kant Baltic Federal University, IKBFU, 14, A. Nevskogo str., Kaliningrad, 236041, Russia



This article presents the results of a thermal model developing and application of a cathode with Barium emitter for the temperature field computing, determining internal and external conductive and radiative heat fluxes, gradients and velocities of temperature changing in the cathode stationary and dynamic operation modes, as well as heat release computing on the cathode emitter. Based on the computational results of the thermal state of the cathode design elements in functioning modes, the analysis of the cathode design and start parameters, which ensure meeting the thermal requirements to its main elements, was performed.

The objectives of the above said thermal computations were:

– determining a minimum power for the cathode pre-start heating, which ensures conditions of reaching emitter temperature within 160 sec (the level sufficient to ignite and maintain the discharge),

– estimating temperature distribution by the cathode elements at various boundary conditions and verifying the thermal model based on the thermal vacuum tests results to employ the model for determining the cathode structure thermal state at various boundary conditions.

The task of the thermal calculation was elements thermal state estimation of the cathode with Barium thermo-emitter in the start heating mode and in the automatic mode (which means the cathode operation when thermo-emitter temperature is maintained by bombarding by the ions of the working body. The discharge circuit between the anode and cathode herewith is closed, and the source of the external heating (heater) is turned-off by way of determining the estimated range and thermal flows over the cathode elements A 3D thermal model of a cathode with Barium emitter was developed with SolidWorks Flow Simulation 2014, which employs the finite volume method, i.e. a numerical method for integration of differential equation systems in partial derivatives. Boundary conditions for the thermal design were being set identical to the thermal vacuum test conditions.

The following elements were set in the model: parts geometrical sizes (with insignificant simplifications not affecting the temperature distribution), structural materials properties and contact thermal resistances between the model areas. The calculation accounted for only conductive and radiative heat exchange, since cathode operation conditions as a part of the thruster represent a deep vacuum. A power, corresponding to the operation mode, was set on the heat releasing elements of the cathode thermal model depending on time and operation mode. When calculating a radiative component of heat exchange, integral emissivity factor was assigned to each surface, depending on material and surface treatment class.

Anisotropic thermal conductivity was set in the ceramic parts properties, i.e. thermal conductivity of Aluminum oxide ceramics is two-directional. Direction of axial (transversal) and radial thermal conductivity ws determined along the corresponding axis of the coordinate system. A temperature dependence between the thermal conductivity coefficient and thermal capacity was accounted for in structural materials properties.

Experimental data obtained at EDB Fakel facility from thermal vacuum tests of a cathode with Barium emitter was employed for the thermal design model verification. The thermal model verification consisted in heaters power selection and heat release on the emitter from the condition that the temperature calculated values in the checkpoints coincide with the measured ones.

Based on the thermal design results, a minimum heater power for guaranteed start of the cathode with Barium emitter was selected.

Cathode thermal model verification with the thermal vacuum test results was carried out. This allows the cathode thermal model application for predicting a thermal state of the cathode structure while numerical reproduction of situations, which were not verified while physical experiment, as well as compare the temperature predictions with the temperatures registered in flight.


cathode-compensator, barium thermal emitter, thermal vacuum tests, thermal model verification, stationary plasma engine, SolidWorks Flow Simulation PPP, cathode design


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