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private:writeups:hallthrusters [2020/07/28 14:33]
admin [Electron transport] 		private:writeups:hallthrusters [2020/08/06 15:59] (current)
admin
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 ====== Instabilities ====== ====== Instabilities ======
  
-Several common low-frequency instabilities in HETs+Several common low-frequency instabilities in HETs.   
 + 
 +Four main instabilities (plus a few lesser observed ones) 
 +  - Breathing mode (m=0 ionization instability) 
 +  - Spoke mode (m>1 ionization instability) 
 +  - Axial transit time oscillations (due to high electron resistivty) 
 +  - Azimuthal $E \times B$ electron drift instabilities (Related to strong $\nabla_z B_r$ gradients) 
 + 
 +Impact HETs by
  
   * these oscillations can indeed lead to violent conditions that could potentially damage the thruster discharge supply   * these oscillations can indeed lead to violent conditions that could potentially damage the thruster discharge supply
   * these oscillations may "provide the necessary electric conductivity for operation [and] this type of oscillation can be considered as useful or normal."  - Zhurin, V., Kahn, J., Kaufman, H., Kozubsky, K., and Day, M.,"Dynamic Characteristics of Closed Drift Thrusters," IEPC-93-095, 23rd International Electric Propulsion Conference, Seattle, WA, 1993.   * these oscillations may "provide the necessary electric conductivity for operation [and] this type of oscillation can be considered as useful or normal."  - Zhurin, V., Kahn, J., Kaufman, H., Kozubsky, K., and Day, M.,"Dynamic Characteristics of Closed Drift Thrusters," IEPC-93-095, 23rd International Electric Propulsion Conference, Seattle, WA, 1993.
 +
 +Sources:
 +
 +  * [Boeuf2017] has a brief recap
 +  * [Choueri2001] has a thorough review but is a little dated
  
  
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   * Strong function of $\frac{B_r}{B_{r,optimal}}$.  This (and honestly most) instabilities are avoided by changing a different parameter space, i.e. B/Bopt.     * Strong function of $\frac{B_r}{B_{r,optimal}}$.  This (and honestly most) instabilities are avoided by changing a different parameter space, i.e. B/Bopt.  
   * Sensitive to correctly designed PPU and matching filter to suppress this mode.     * Sensitive to correctly designed PPU and matching filter to suppress this mode.  
 +
 +[Boeuf2017] 
 +  * 10-20 kHz range
 +  * "Reasonably well understood"
 +  * Due to strong ionization of the atom flow in the large magnetic field region, the neutral atom front moves upstream in a lower magnetic field region where ionization becomes less efficient because the electron mobility is larger. This leads to a decrease of the current till the neutral atom front moves back to the exhaust region where intense ionization can take place again. This oscillation mode has been termed as “breathing mode”
 +  * Period of oscillation is related to the time necessary for neutrals to replenish the ionization region.
 +  * Can be modeled (with many simplifications) as a predator-prey system of neutrals and ions. The result is a harmonic oscillator.  TODO - Find derivation and put here.  
  
 [Fife1997] [Fife1997]
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   * Oscillating azimuthal electric field creates a $ v_z=$ $\frac{E_\theta \times B_r }{B_r^2}$ $=\frac{E_\theta}{B_r}$ axial drift velocity that is part of the ``anomalous transport" mechanism that causes electrons to more rapidly escape confinement.     * Oscillating azimuthal electric field creates a $ v_z=$ $\frac{E_\theta \times B_r }{B_r^2}$ $=\frac{E_\theta}{B_r}$ axial drift velocity that is part of the ``anomalous transport" mechanism that causes electrons to more rapidly escape confinement.  
   * Claims the detailed physics describing this instability are poorly explored.  (Is this still correct?)   * Claims the detailed physics describing this instability are poorly explored.  (Is this still correct?)
 +
 +[Boeuf2017]
 +  * density fluctuations moving azimuthally in the direction of the electron drift with a phase velocity of 0.2E/B.
 +  * Dominant in the anode region
 +  * plasma potential in that region appears to fluctuate in a helical fashion and that this could also play a role in driving cross-field electron transport
 +  * A non-zero fluctuating azimuthal electric field $E_\theta$ results in an $E_\theta \times B_r$ axial drift.  Assuming, $E_\theta = E_0 sin(\theta)$ and $n=n0 + n1 \ sin(\theta+\phi)$, the axial electron current density is $J=e\int n \frac{E\theta}{B} dA/A$.  Plugging in and solving, the current becomes $J= e n_1 \frac{E_0}{B_r}cos(\phi)$
 +  * Nature of this instability is not completely clear.  
 +  * The CIV (Critical Ionization Velocity) concept implies that the rotation of the spoke is associated with a rotating double layer (charge separation) with an azimuthal potential drop on the order of the ionization energy of the gas, 
 +  * the presence of spokes does not seem to affect the performance of the thruster because it primarily effects the region near the anode and NOT the acceleration region.  
  
 [Me] [Me]
   * Maybe another way to think of this is an azimuthally rotating ionization region with an azimuthal structure $exp \left( i(m\theta - \omega t) \right) $ where the mode number, $m$, is an integer greater than 0.     * Maybe another way to think of this is an azimuthally rotating ionization region with an azimuthal structure $exp \left( i(m\theta - \omega t) \right) $ where the mode number, $m$, is an integer greater than 0.  
  
-==== 3. Azimuthal drift instability related to axial gradients in $\nabla_z B_r$ ====+==== 3. Azimuthal $E \times B$ drift instability related to axial gradients in $\nabla_z B_r$  ====
  
  
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   * For the purpose of stability, $\nabla_z B_r$ is designed to be positive along the discharge chamber, with the minimum magnetic field at the anode and maximum near the exit plane.   * For the purpose of stability, $\nabla_z B_r$ is designed to be positive along the discharge chamber, with the minimum magnetic field at the anode and maximum near the exit plane.
  
 +[Boeuf2017] 
 +  * large amplitude, small wavelength azimuthal oscillations of the azimuthal electric field
 +  * result from the coupling between electron Bernstein waves and ion acoustic waves
  
-==== 4. Poorly understood ... ==== 
  
-[Choueiri2001]  +==== 4. Axial "Transient-time" oscillations ====
-  * Typically 20 to 100 kHz +
-  * Non-azimuthal +
-  * Poorly reported in literature, partially because of the overlap with the previous azimuthal instabilities. +
-  * Thought to be related to 1) neutral collisions or 2) ionization.   +
- +
- +
-==== 5. Axial "Transient-time" oscillations ====+
  
 [Choueiri2001]  [Choueiri2001] 
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   * Well predicted by linear theory of gradient driven magnetosonic waves with a primarily axial propagation   * Well predicted by linear theory of gradient driven magnetosonic waves with a primarily axial propagation
   * Due to the coupling of the "beam mode" ($k_z u_i$) with $\nabla_z B_r$ driven oscillations.     * Due to the coupling of the "beam mode" ($k_z u_i$) with $\nabla_z B_r$ driven oscillations.  
 +
 +[Boeuf2017] 
 +  * 100 to 500 kHz
 +  * associated with the transit time of ions in the acceleration region 
 +  * The dispersion relation for these waves can be obtained by writing and linearizing a system of 1D fluid equations based on electron and ion continuity equations, collisionless momentum equation for cold ions, and a drift-diffusion momentum equation for electrons, with the constraint of constant current.  further simplified by removing the effect of ionization and electron pressure leading to the resistive mode
 +  * amplitude of the oscillations was strongly dependent on the electron resistivity and increased with decreasing electron mobility, in total agreement with the resistive mode
 +  * associated with important kinetic effects coupled with oscillations of the acceleration zone
 +  * During the oscillations of the acceleration zone, some ions may “see” a total potential drop larger than the applied voltage while a group of low energy ions is formed.
 +  * due to a too large electron resistivity
 +
 +[Me]
 +  * The dependence on large electron resistivity to me is counter intuitive.  I'm used to resistivity damping oscillations, not exciting them.  
 +
 +==== 5. Poorly understood and unnamed instability ... ====
 +
 +[Choueiri2001] 
 +  * Typically 20 to 100 kHz
 +  * Non-azimuthal
 +  * Poorly reported in literature, partially because of the overlap with the previous azimuthal instabilities.
 +  * Thought to be related to 1) neutral collisions or 2) ionization.  
 +
  
  
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 ====== Magnetic field design ======= ====== Magnetic field design =======
  
-  * [Hofer2014]   While a complete understanding of electron dynamics is currently unavailable, it is known that the electron dynamics can be influenced by controlling the shape and strength of the magnetic field. At least in this sense, it is fair to say that the magnetic field is the most important aspect+[Hofer2014]    
 +  * While a complete understanding of electron dynamics is currently unavailable, it is known that the electron dynamics can be influenced by controlling the shape and strength of the magnetic field. At least in this sense, it is fair to say that the magnetic field is the most important aspect
 of Hall thruster design. of Hall thruster design.
  
 +[Bouef2017]  
 +  * The radial electric field (location and magnitude) is directly related to 
 +    - Electron transport 
 +    - electric field distribution 
 +    - ionization 
 +    - ion beam divergence through the potential distribution (I don't get this) 
 +    - Wall erosion by ions
 ====== Open issues related to HETs ====== ====== Open issues related to HETs ======
 (Need citations...) (Need citations...)
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   - Improving ground based models/experiments to successfully predict space operation   - Improving ground based models/experiments to successfully predict space operation
   - etc   - etc
 +
 +
 +====== Probes and other diagnostics ======
 +The goal of this section is to list common (or even uncommon) diagnostics associated with measuring "anything" in a Hall thruster.  
 +
 +  * Laser Induced Fluorescence (LIF) - Measures ion and atom (presumably neutral?) mean velocity.  [Boeuf2017].  Used to study instabilities (oscillations in velocity) [Boeuf2017].
 +  * Langmuir probes - temperature, density, plasma potential
 +  * Segmented electrodes - Used to study instabilities (need specifics) [Boeuf2017].
 +  * "Fast imaging probes" - Used to study instabilities (need specifics) [Boeuf2017].  I don't know what this probe actually is.  
 +  * Discharge current measurements - Measurement of total current, I_elec + I_ion.  Also used to study instabilities (as instabilities causes oscillations in conductivity).  
 +  * Highspeed videos of exhaust.  Image is on-axis.  - Used to study spoke instabilities.  
 +
 +
 +====== Ionization region ======
 +
 +==== Length of ionization region ====
 +
 +[Boeuf2017] 
 +  * TODO
 +
  
 ====== Questions ====== ====== Questions ======
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   * I've seen mixed comments as to whether "axial electron transport" is all bad or whether "there are cases where electron transport actually improve".  Thoughts?   * I've seen mixed comments as to whether "axial electron transport" is all bad or whether "there are cases where electron transport actually improve".  Thoughts?
   * [Boeuf2017] As the thruster size and power change, the current density does not change and stays on the order of 1000 A/m^2 in most Hall thrusters.  Why?   * [Boeuf2017] As the thruster size and power change, the current density does not change and stays on the order of 1000 A/m^2 in most Hall thrusters.  Why?
 +  * Would secondary electrons generated by electron striking channel walls be an alternative source of electrons?  
 +  * There's something to the equipotential argument in E and B that I'm not quite following.  
private/writeups/hallthrusters.1595946834.txt.gz · Last modified: 2020/07/28 14:33 by admin

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