Editing Hall-effect thruster (section)

== Principle of operation ==
The essential working principle of the Hall thruster is that it uses an [[electrostatic potential]] to accelerate ions up to high speeds.  In a Hall thruster, the attractive negative charge is provided by an electron plasma at the open end of the thruster instead of a grid.  A radial magnetic field of about {{cvt|100|–|300|G|mT|lk=on}} is used to confine the electrons, where the combination of the radial magnetic field and axial electric field cause the electrons to drift in azimuth thus forming the Hall current from which the device gets its name.

[[File:Wfm hall thruster.svg|thumb|upright=1.8|Hall thruster. Hall thrusters are largely axially symmetric. This is a cross-section containing that axis.]]
A schematic of a Hall thruster is shown in the adjacent image. An [[electric potential]] of between 150 and 800 volts is applied between the [[anode]] and [[cathode]].

The central spike forms one pole of an [[electromagnet]] and is surrounded by an annular space, and around that is the other pole of the electromagnet, with a radial magnetic field in between.

The propellant, such as [[xenon]] gas, is fed through the anode, which has numerous small holes in it to act as a gas distributor. As the neutral xenon atoms diffuse into the channel of the thruster, they are ionized by collisions with circulating high-energy electrons (typically 10–40&nbsp;eV, or about 10% of the discharge voltage). Most of the xenon atoms are ionized to a net charge of +1, but a noticeable fraction (c. 20%) have +2 net charge.

The xenon ions are then accelerated by the [[electric field]] between the anode and the cathode. For discharge voltages of 300&nbsp;V, the ions reach speeds of around {{cvt|15|km/s|mi/s}} for a specific impulse of 1,500&nbsp;s (15&nbsp;kN·s/kg). Upon exiting, however, the ions pull an equal number of electrons with them, creating a [[plasma (physics)|plasma]] plume with no net charge.

The radial magnetic field is designed to be strong enough to substantially deflect the low-mass electrons, but not the high-mass ions, which have a much larger [[gyroradius]] and are hardly impeded.  The majority of electrons are thus stuck orbiting in the region of high radial magnetic field near the thruster exit plane, trapped in ''E''×''B'' (axial electric field and radial magnetic field). This orbital rotation of the electrons is a circulating [[Hall effect|Hall current]], and it is from this that the Hall thruster gets its name.  Collisions with other particles and walls, as well as plasma instabilities, allow some of the electrons to be freed from the magnetic field, and they drift towards the anode.

About 20–30% of the discharge current is an electron current, which does not produce thrust, thus limiting the energetic efficiency of the thruster; the other 70–80% of the current is in the ions. Because the majority of electrons are trapped in the Hall current, they have a long residence time inside the thruster and are able to ionize almost all of the xenon propellant, allowing mass use of 90–99%. The mass use efficiency of the thruster is thus around 90%, while the discharge current efficiency is around 70%, for a combined thruster efficiency of around 63% (= 90% × 70%). Modern Hall thrusters have achieved efficiencies as high as 75% through advanced designs.

Compared to chemical rockets, the thrust is very small, on the order of 83&nbsp;mN for a typical thruster operating at 300&nbsp;V and 1.5&nbsp;kW. For comparison, the weight of a coin like the [[quarter (U.S. coin)|U.S. quarter]] or a 20-cent [[euro coin]] is approximately 60&nbsp;mN. As with all forms of [[electrically powered spacecraft propulsion]], thrust is limited by available power, efficiency, and [[specific impulse]].

However, Hall thrusters operate at the high [[specific impulse]]s that are typical for electric propulsion. One particular advantage of Hall thrusters, as compared to a [[gridded ion thruster]], is that the generation and acceleration of the ions takes place in a quasi-neutral plasma, so there is no [[Space charge|Child-Langmuir charge]] (space charge) [[saturation current|saturated current]] limitation on the thrust density. This allows much smaller thrusters compared to gridded ion thrusters.

Another advantage is that these thrusters can use a wider variety of propellants supplied to the anode, even oxygen, although something easily ionized is needed at the cathode.<ref>{{Cite web|url = http://www.permanent.com/space-transportation-electric.html#how-russ|title = Hall-Effect Stationary Plasma thrusters|access-date = 16 June 2014|website = Electric Propulsion for Inter-Orbital Vehicles|url-status = live|archive-url = https://web.archive.org/web/20130717081003/http://www.permanent.com/space-transportation-electric.html#how-russ|archive-date = 17 July 2013}}[http://www.permanent.com/t-el-iov.htm#how-russ <!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20071010015756/http://www.permanent.com/t-el-iov.htm|date=10 October 2007 }}</ref>

=== Propellants ===

==== Xenon ====
[[Xenon]] has been the typical choice of propellant for many electric propulsion systems, including Hall thrusters.<ref name="auto">{{Cite web|title=Krypton Hall effect thruster for spacecraft propulsion|url=https://www.sciencedaily.com/releases/2011/10/111006084023.htm|access-date=28 April 2021|website=ScienceDaily|language=en}}</ref> Xenon propellant is used because of its high [[atomic weight]] and low [[ionization potential]]. Xenon is relatively easy to store, and as a gas at spacecraft operating temperatures does not need to be vaporized before usage, unlike metallic propellants such as bismuth. Xenon's high atomic weight means that the ratio of energy expended for ionization per mass unit is low, leading to a more efficient thruster.<ref>{{Cite web|title=Hall Thruster Project|url=https://w3.pppl.gov/~fisch/hall_thruster_project4.htm|access-date=28 April 2021|website=w3.pppl.gov}}</ref>

==== Krypton ====
[[Krypton]] is another choice of propellant for Hall thrusters. Xenon has an ionization potential of 12.1298 eV, while krypton has an ionization potential of 13.996 eV.<ref name="lenntech">{{Cite web|title=The elements of the periodic table sorted by ionization energy|url=https://www.lenntech.com/periodic-chart-elements/ionization-energy.htm|access-date=28 April 2021|website=www.lenntech.com}}</ref> This means that thrusters utilizing krypton need to expend a slightly higher energy per mole to ionize, which reduces efficiency. Additionally, krypton is a lighter ion, so the unit mass per ionization energy is further reduced compared to xenon. However, xenon can be more than ten times as expensive as krypton per [[kilogram]], making krypton a more economical choice for building out [[Satellite constellation|satellite constellations]] like that of [[SpaceX]]'s [[Starlink]] V1, whose original Hall thrusters were fueled with krypton.<ref name="auto" /><ref name=":0" />

==== Argon ====
[[SpaceX]] developed a new thruster that used [[argon]] as propellant for their [[Starlink]] V2 mini. The new thruster had 2.4 times the thrust and 1.5 times the specific impulse as [[SpaceX]]'s previous thruster that used krypton.<ref name="sn-20230228" /> Argon is approximately 100 times less expensive than Krypton and 1000 times less expensive than Xenon.<ref>{{cite book |author1=Shuen-Chen Hwang |first2=Robert D. |last2=Lein |first3=Daniel A. |last3=Morgan |date=2005 |title=Kirk Othmer Encyclopedia of Chemical Technology |chapter=Noble Gases |doi=10.1002/0471238961.0701190508230114.a01 |pages=343–383 |publisher=Wiley |isbn=978-0-471-23896-6 }}</ref>

==== Comparison of noble gasses ====
{| class="wikitable sortable wide"
|+ Noble gas properties and cost comparison table
|-
! Gas !! Symbol !! at wt (g/mol) !! ionization potential (eV) <ref name="lenntech" /> !! unit mass per ionization energy 
! reference price<ref>{{Cite web|title=Chemical elements by market price|url=http://www.leonland.de/elements_by_price/en/list|access-date=17 September 2023|language=en}} Using the Reference Price column, as the cost per unit weight values are inconsistent. The table provides dates that appear to be when quotes were obtained, but has links only to generic supplier websites.</ref>
! cost / m³ (€) !! density (g/l) !! cost / kg (€) !! relative to cheapest
|-
!
!
!
!
!
!
!
!
!
!
|-
| [[Xenon]] || Xe || 131.29 || 12.13 || 10.824 || 25 € / l || 25000 || 5.894 || 4241.60 || 1905
|-
| [[Krypton]] || Kr || 83.798 || 14.00 || 5.986 || 3 € / l || 3000 || 3.749 || 800.21 || 359
|-
| [[Argon]] || Ar || 39.95 || 15.81 || 2.527 || $0.12 / ft³ || 3.97 || 1.784 || 2.23 || 1
|-
| [[Neon]] || Ne || 20.18 || 21.64 || 0.933 || € 504 / m³ || 504 || 0.9002 || 559.88 || 251
|-
| [[Helium]] || He || 4.002 || 24.59 || 0.163 || $7.21 / m³ || 6.76 || 0.1786 || 37.84 || 17
|}


=== Variants ===
As well as the Soviet SPT and TAL types mentioned above, there are: 

====Cylindrical Hall thrusters====
[[File:Hall Effect Thruster in a vacuum chamber.jpg|thumb|An Exotrail ExoMG – nano (60&nbsp;W) Hall Effect Thruster firing in a vacuum chamber]]

Although conventional (annular) Hall thrusters are efficient in the [[kilowatt]] power regime, they become inefficient when scaled to small sizes. This is due to the difficulties associated with holding the performance scaling parameters constant while decreasing the channel size and increasing the applied [[magnetic field]] strength. This led to the design of the cylindrical Hall thruster. The cylindrical Hall thruster can be more readily scaled to smaller sizes due to its nonconventional discharge-chamber geometry and associated [[magnetic field]] profile.<ref>{{cite web|first1=Y. |last1=Raitses |first2=N. J. |last2=Fisch |title=Parametric Investigations of a Nonconventional Hall Thruster|url=http://htx.pppl.gov/publication/Journal/CHT_PoP_2001.pdf|publisher=Physics of Plasmas, 8, 2579 (2001)|url-status=live|archive-url=https://web.archive.org/web/20100527094903/http://htx.pppl.gov/publication/Journal/CHT_PoP_2001.pdf|archive-date=27 May 2010}}</ref><ref>{{cite web|first1=A. |last1=Smirnov |first2=Y. |last2=Raitses |first3=N. J. |last3=Fisch |title=Experimental and theoretical studies of cylindrical Hall thrusters|url=http://htx.pppl.gov/publication/Journal/CHT_Artem_PoP2007.pdf|publisher=Physics of Plasmas 14, 057106 (2007)|url-status=live|archive-url=https://web.archive.org/web/20100527095129/http://htx.pppl.gov/publication/Journal/CHT_Artem_PoP2007.pdf|archive-date=27 May 2010}}</ref><ref name=NTRS>{{cite conference |last1=Polzin |first1=K. A.|last2=Raitses |first2=Y. |last3=Gayoso |first3=J. C. |last4=Fisch |first4=N. J. |title=Comparisons in Performance of Electromagnet and Permanent-Magnet Cylindrical Hall-Effect Thrusters |conference=46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference |website=NASA Technical Reports Server|date=25 July 2010 |hdl=2060/20100035731 |hdl-access=free}}</ref> The cylindrical Hall thruster more readily lends itself to miniaturization and low-power operation than a conventional (annular) Hall thruster. The primary reason for cylindrical Hall thrusters is that it is difficult to achieve a regular Hall thruster that operates over a broad envelope from c.1&nbsp;kW down to c. 100&nbsp;W while maintaining an efficiency of 45–55%.<ref>{{cite conference |last1=Polzin |first1=K. A. |last2=Raitses |first2=Y. |last3=Merino |first3=E. |last4=Fisch |first4=N. J. |title=Preliminary Results of Performance Measurements on a Cylindrical Hall-Effect Thruster with Magnetic Field Generated by Permanent Magnets |conference=3rd Spacecraft Propulsion Subcommittee (SPS) meeting/JANNAF Interagency Propulsion Committee |website=NASA Technical Reports Server|date=8 December 2008 |hdl=2060/20090014067 |hdl-access=free}}</ref>

====External discharge Hall thruster====
Sputtering erosion of discharge channel walls and pole pieces that protect the magnetic circuit causes failure of thruster operation. Therefore, annular and cylindrical Hall thrusters have limited lifetime. Although magnetic shielding has been shown to dramatically reduce discharge channel wall erosion, pole piece erosion is still a concern.<ref>{{Cite book |chapter=Pole-piece Interactions with the Plasma in a Magnetically Shielded Hall Thruster |title=50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference |doi=10.2514/6.2014-3899 |isbn=978-1-62410-303-2 |date=2014 |last1=Goebel |first1=Dan M. |last2=Jorns |first2=Benjamin |last3=Hofer |first3=Richard R. |last4=Mikellides |first4=Ioannis G. |last5=Katz |first5=Ira }}</ref> As an alternative, an unconventional Hall&nbsp;thruster design called external discharge Hall thruster or external discharge plasma thruster (XPT) has been introduced.<ref>{{Cite book |chapter=Preliminary Investigation of an External Discharge Plasma Thruster |title=52nd AIAA/SAE/ASEE Joint Propulsion Conference |doi=10.2514/6.2016-4951 |isbn=978-1-62410-406-0 |date=2016 |last1=Karadag |first1=Burak |last2=Cho |first2=Shinatora |last3=Oshio |first3=Yuya |last4=Hamada |first4=Yushi |last5=Funaki |first5=Ikkoh |last6=Komurasaki |first6=Kimiya }}</ref><ref>{{Cite web|url=https://repository.exst.jaxa.jp/dspace/bitstream/a-is/549895/1/SA6000036090.pdf|title=Numerical Investigation of an External Discharge Hall Thruster Design Utilizing Plasma-lens Magnetic Field|url-status=live|archive-url=https://web.archive.org/web/20170814095202/https://repository.exst.jaxa.jp/dspace/bitstream/a-is/549895/1/SA6000036090.pdf|archive-date=14 August 2017}}</ref><ref>{{Cite web|url=http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1037721&dswid=1358|title=Low–voltage External Discharge Plasma Thruster and Hollow Cathodes Plasma Plume Diagnostics Utilising Electrostatic Probes and Retarding Potential Analyser|url-status=live|archive-url=https://web.archive.org/web/20170829163334/http://ltu.diva-portal.org/smash/record.jsf?pid=diva2%3A1037721&dswid=1358|archive-date=29 August 2017}}</ref> The external discharge Hall thruster does not possess any discharge channel walls or pole pieces. Plasma discharge is produced and sustained completely in the open space outside the thruster structure, and thus erosion-free operation is achieved.