Jul 15

Surface-bound hydrogen: diffusion > desorption

Wait! What? “The first step in hydrogen storage is chemisorption, wherein gaseous H2 collides with Pd and adsorbs (sticks) to the surface. Secondly, the chemisorbed H atoms diffuse into the sub-surface, several nanometers deep.”

Why gold-palladium alloys are better than palladium for hydrogen storage

Jul 14

Improvizing a history

If you’re willing to listen some Turkish music, here we go! This song means a lot me but also it is hard to explain. To me, it is about the changes happening without our interventions. I’ve played this song many times so I have tons of versions of the same song.

Soft version:

Hard version:

Jul 14


In this article, Otway provides a solution to the closed Dirichlet problem which is a mixed eliptic-hyperbolic equation. This type of equations are encountered in electromagnetic wave propagation in cold plasmas. The equation in the model for electromagnetic wave propagation in zero-temperature plasma is:

(x-y^2)u_{xx}+u_{yy}+\kappa u_{x}=0

where u(x,y) is twice-continuously differentiable function. This is a homogeneous closed Dirichlet problem with D-star-shaped domains. To determine the boundary conditions, a geometric or physical analogy is considered to solve the equation. The boundary arcs are good approximations to produce an appropriate vector field. Although this approach is introduced by Lupo and Payne, the results of this study generalize the starlike boundary conditions to elliptic-hyperbolic boundary value problems. Before this study, the closed Dirichlet problems are considered as ill-posed. However, the author describes a novel method to solve the problem by presenting a unique weak solution with suitable weight function. The weight function is determined as y=x^2 and it reduces to y=0 when uniqueness is eliminated. Physically, it refers to a heating point in the plasma satisfying the equation itself.

image credit: Visual Mathematics – Math in Art – Works in Progress (Geometry and Topology)

The unstable heating on plasmas creates anisotropy for electromagnetic waves. The field potential in inhomogeneous regions can be represented as Equation 1. By reducing the number of hybrid waves in the plasma, an unstable heating solution can be obtained with kappa=0. The function domain Omega is defined as open, bounded and connected. The boundary condition is decided as:

u(x,y)=0 for all (x,y) in Omega.

In the study, it is shown that there is a solution to a closed Dirichlet problem by proving the existence of L^2 solutions where L is differential operator, such that:


where K(x,y)=x-y^2. The advantage of this approach is that a homogeneous equation with singularity is converted into an inhomogeneous equation by avoiding trivial solutions with known f(x,y).

For the weak solution, the problem is simplified by ignoring kappa. The general solution can be obtained by defining u=(u_1(x,y),u_2(x,y)). For this strong solution, K(x,y)=x-sigma(y) is chosen.

(Lu)_1=[x-\sigma(y)]u_{1x}+u_{2y}+\kappa_1u_1+\kappa_2u_2  and  (Lu)_2=u_{1y}-u_{2x}

where kappa_1 and kappa_2 are constants. The reduced forms of these equations imply Cinquini-Cibrario equation which presents applicable models for atmospheric and space plasmas.

The article is well-explained in terms of the clarity of the mathematical methods; however, the author failed to recognize the physical phenomena, described here as the wave propagation in the plasma. The article could include precisely the temperature level interested and the pressure dependence of plasma waves. The derivation is conducted at zero temperature by neglecting fluid properties. The Maxwell equations are derived for the electric displacement vector. Still, those who are interested in solving elliptic-hyperbolic equations would benefit from this article by approaching to the closed Dirichlet problems with different boundary conditions.

*Latex format will be updated.


Otway, Thomas H.,2010, Unique solutions to boundary value problems in the cold plasma model, SIAM Journal on Applied Mathematics, 42(6): 3045-3053.

Lupo, D. and Payne, K.R., 2003. Critical exponents for semilinear equations of mixed elliptic‐hyperbolic and degenerate types. Communications on pure and applied mathematics, 56(3), pp.403-424.

Jul 14

Experimental Study of the Effects of the Cathode Position and the Electrical Circuit Configuration on the Operation of HK40 Hall Thruster and BUSTLab Hollow Cathode

HK40 Hall thruster, designed and developed at the Bogazici University Space Technologies Laboratory (BUSTLab), is an SPT type Hall thruster with a 40 mm discharge channel. HK40 was initially designed to operate with SmCo permanent magnets. To optimize the magnetic field topology, the permanent magnets were replaced with iron-core electromagnets. The thruster is operated with different magnetic coil currents to observe the changes in discharge characteristics. Magnetic field topology of the thruster is examined to determine the proper location of a LaB6 hollow cathode, which is also designed and built at BUSTLab. External magnetic field topology of a Hall thruster has an important characteristic called magnetic field separatrix defining the boundary between closed magnetic surfaces and open magnetic field lines. To investigate the effects of the separatrix surfaces, the location of the cathode is changed in-situ with respect to the Hall thruster with a 2-D translational stage in two different grounding configurations, one connecting the vacuum chamber to the same ground with the power supplies, and the other with the power supplies connected to a common floating ground. We show that the influence of the external magnetic field strength on the thruster efficiency can be predicted from the electron current coming from the cathode emitter surface. We also show that the cathode to ground voltage provides a way to estimate the efficiency with respect to the cathode placement. The mechanisms and the efficiency values of two setups are compared to explain the ground and the space operations.

You can reach this paper with the following link:

Joint Propulsion Conference and Exhibit (JPC), Salt Lake City, Utah, USA, 25–27 July 2016, AIAA-2016-4834.

Some figures from the paper:



Electrical schematic for the floating setup with a common ground




Electrical schematic for the grounded setup




Magnetic contours of HK40 Hall thruster inside the BUSTLab vacuum chamber

Jul 14

Experimental Investigation of the Effects of Cathode Current on HK40 Hall Thruster Operation

Hall effect thrusters utilize electric and magnetic fields to extract ions from a plasma discharge. The cathode is responsible for the ionization of the propellant and the neutralization of the ion beam by emitting an equal number of electrons to prevent spacecraft charging. Hollow cathode electrons are extracted from LaB6 insert surface by thermionic emission. The electrons leaving the surface generate a negative cathode voltage around LaB6 emitter. As the emitter surface expels electrons, the same amount of electrons are attracted from the ground. Those electrons are measured as the ground current. For Hall effect thrusters, the electron movements are determined by the external magnetic lines of the thruster. If electrons could not pass the magnetic field lines, they could not reach the anode and the magnitude of cathode to ground voltage increases. As a result, plume plasma potential increases. This study shows that by measuring the electron current coming from the emitter surface, influence of the external magnetic field strength on the efficiency of the thruster could be predicted.

You can reach this paper with the following link:

5th International Conference on Space Propulsion, Rome, Italy, 2-6 May 2016, SP2016-3125333.

Some figures from the paper:



Schematic of the paths of electrons with ionization



Electrons trapped in the discharge channel by the magnetic field

Jul 14

Investigation of the Effect of Hollow Cathode Neutralizer Location on Hall Effect Thruster Efficiency

Neutralization of ions is important for all electric thruster types when considering thruster efficiency and life. Hollow cathode is responsible for both creating plasma discharge and neutralization of the beam ions for Hall Effect Thruster (HET). In this study, appropriate placement of the cathode is investigated by taking into account that the decrease in cathode coupling voltage increases thruster efficiency. Regarding this, the effects of mass flow rate of the cathode and keeper current on the coupling voltage are investigated, according to available experimental results from the literature.

You can reach this paper with the following link:

7th International Conference on Recent Advances in Space Technologies (RAST), Istanbul, Turkey, 16-19 June 2015.

Some figures from the paper:


Jul 14

Note: Coaxial-heater hollow cathode

The design and tests of a LaB6 hollow cathode with a novel heater are presented. In the new design, the heater wire is completely encapsulated around the cathode tube and a coaxial return electrode, thereby eliminating hot spots on the heater wire due to the free hanging regions. Since the new heater confines the Joule heating to the region of interest, where the LaB6 emitter is placed, the heater terminals are further secured from overheating. The cathode with the presented heater design has been successfully tested and is able to deliver currents in the 0.5-15 A range.


You can reach this paper with the following link:

Kurt, H.; Turan, N.; Kokal, U.; Celik, M. “Note: Coaxial-heater Hollow Cathode”, Review of Scientific Instruments, Vol. 88, No. 6, pg. 066103, 2017.

Some figures from the paper:


2D cross-sectional drawing of the coaxial hollow cathode

Jul 14

Music? YES!

As a huge Alice in Chains fan, I’m picking a song and improvising it.

Jul 14

Thermal Analysis and Testing of Different Designs of Lanthanum Hexaboride Hollow Cathodes

Electric propulsion systems provide a higher delta-V for the same mass of propellant when compared to chemical propulsion systems due to their higher Isp levels. Many electric propulsion systems utilize cathodes as electron source. Hollow cathodes generate electron current through thermionic emission mechanism. In this study conventional hollow cathode designs are investigated numerically and experimentally. Considering the problems that are encountered with the conventional designs, a new hollow cathode design is developed, which is called coaxial hollow cathode. Operational parameters of the coaxial cathode are investigated experimentally.

You can reach this paper with the following link:

8th International Conference on Recent Advances in Space Technologies (RAST), 19-22 June 2017.

Some figures from the paper:


Heat Flux, Top: First conventional heater design, Middle: Second conventional heater design, Bottom: Coaxial hollow cathode design


Temperature distribution, Top: First conventional heater design, Middle: Second conventional heater design, Bottom: Coaxial hollow cathode design

Jul 14

Development of the New BUSTLab Hall Thruster with Internal Coaxial Hollow Cathode

HK40 Hall thruster is a low power SPT-type Hall thruster with a boron nitride (BN)
discharge channel of 40 mm in outer diameter. Based on the experience gained during the design and manufacturing of the HK40 Hall thruster, and the experiments that were conducted with this Hall thruster, an advanced larger diameter Hall thruster with an LaB6 internal cathode is developed. In the design, protection of thruster wall material is aimed by the appropriate magnetic field inside the thruster channel. Design optimization of this new Hall thruster is made by investigating the effects of different design parameters, such as magnetic circuit and discharge channel geometry. A thermal model of this thruster is developed in order to investigate the heat distribution for the thruster-cathode system.

You can reach this paper with the following link:

53rd Joint Propulsion Conference, Atlanta, GA, July 2017, also AIAA-2017-4810.

Some figures from the paper:


Operational parameters and dimensions of various thrusters


a) 3D drawing of Hall thruster with internal cathode, b) Cross-sectional view of Hall thruster with
internal cathode

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