Editing Magnetic sail (section)

== Modes of operation ==
Magnetic sail modes of operation cover the mission profile and plasma environment (''pe''), such as the [[solar wind]], (''sw'') a planetary ionosphere (''pi'') or magnetosphere (''pm''), or the [[interstellar medium]] (''ism''). Symbolically equations in this article use the ''pe'' acronym as a subscript to generic variables, for example as described in this section the plasma mass density <math>\rho_{pe}</math> and from the spacecraft point of view the apparent wind velocity <math>u_{pe}</math>.

=== Plasma mass density and velocity terminology and units ===
A [[Plasma (physics)|plasma]] consists exclusively of charged particles that can interact with a magnetic or electric field. It does not include neutral particles, such as neutrons. atoms or molecules.The plasma mass density ρ used in magnetohydrodynamic models only require a weighted average mass density of charged particles that includes neutrons in the ion, while kinematic models use the values for each specific ion type and in some cases the parameters for electrons as well as detailed in the [[#Magnetohydrodynamic model|Magnetohydrodynamic model]] section.

The velocity distribution of ions and electrons is another important parameter but often analyses use only the average velocity for the aggregate of particles in a plasma wind for a particular plasma environment (pe) is <math>v_{pe}</math>. The apparent wind velocity <math>u_{sc}</math> as seen by a spacecraft traveling at velocity <math>v_{sc}</math> (positive meaning acceleration in the same direction as the wind and negative meaning deceleration opposite the wind direction) for a particular plasma environment (''pe'') is <math>u_{sc}=v_{pe}-v_{sc}</math>.

=== Acceleration/deceleration in a stellar plasma wind ===
Many designs, analyses, simulations and experiments focus on using a magnetic sail in the [[solar wind]] plasma to accelerate a spacecraft away from the Sun.<ref name=":0">{{Cite journal |last=Djojodihardjo |first=Harijono |date=21 November 2018 |title=Review of Solar Magnetic Sailing Configurations for Space Travel |url=https://www.researchgate.net/publication/329103132 |journal=Advances in Astronautics Science and Technology |volume=2018 |issue=1 |pages=207–219 |bibcode=2018AAnST...1..207D |doi=10.1007/s42423-018-0022-4 |s2cid=125294757|doi-access=free }}</ref> Near the Earth's orbit at 1 AU the plasma flows at velocity <math>v_{sw}</math> dynamically ranges from 250 to 750&nbsp;km/s (typically 500), with a density ranging from 3 to 10 particles per cubic centimeter (typically 6) as reported by the NOAA real-time solar wind tracking web site<ref>{{Cite web |last=NOAA |date= |title=REAL TIME SOLAR WIND |url=https://www.swpc.noaa.gov/products/real-time-solar-wind |access-date=June 12, 2022}}</ref> Assuming that 8% of the solar wind is helium and the remainder hydrogen, the average solar wind plasma mass density at 1 AU is <math>4\times10^{-21}<\rho_{sw}(1)<10^{-20}</math> kg/m<sup>3</sup> (typically 10<sup>−20</sup> kg/m<sup>3</sup>).<ref>{{Cite web |date=June 29, 2022 |title=Solar Wind |url=https://umbra.nascom.nasa.gov/spartan/the_solar_wind.html |access-date=June 29, 2022 |website=umbra.nascom.nasa.gov}}</ref>

The average plasma mass density of ions <math>\rho_{sw}</math> decreases according to an [[Inverse-square law]] with the distance from the Sun as stated by Andrews/Zubrin<ref name=":4" />  and Borgazzi.<ref name=":32" /> The velocity for values near the Sun is nearly constant, falling off slowly after 1 AU<ref name=":32">{{Cite journal |last1=Borgazzi |first1=A. |last2=Lara |first2=A. |last3=Echer |first3=E. |last4=Alves |first4=M. V. |date=May 2009 |title=Dynamics of coronal mass ejections in the interplanetary medium |url=http://www.aanda.org/10.1051/0004-6361/200811171 |journal=Astronomy & Astrophysics |volume=498 |issue=3 |pages=885–889 |bibcode=2009A&A...498..885B |doi=10.1051/0004-6361/200811171 |issn=0004-6361}}</ref>{{Rp|location=Fig 5}} and then rapidly decreases at [[Heliosphere#Edge structure|heliopause]].

=== Deceleration in interstellar medium (ISM) ===
A spacecraft accelerated to very high velocities by other means, such as a fusion rocket or laser pushed lightsail, can decelerate even from relativistic velocities without onboard propellant by using a magnetic sail to create thrust (drag) against the interstellar medium plasma environment.  As shown in the section on [[#Magsail kinematic model (MKM)|Magsail kinematic model (MKM)]], feasible uses of this involve maximum velocities below 10% [[speed of light|c]], taking decades to decelerate, for total travel times on the order of a century as described in the [[#Specific designs and mission profiles|magsail specific designs]] section.<!-- DM: Not sure if this is synthesis. "Hence this would work best for very long duration missions." Need to find a reference that actually states this. --> [[File:The Local Interstellar Cloud and neighboring G-cloud complex.svg|thumb|upright=1.35]]
Only the magsail references consider deceleration in the ISM on approach to Alpha (<math>\alpha</math>) Centauri, which as shown in the figure is separated by the [[Local Bubble|local bubble]] and the [[G-Cloud|G-clouds]] and the [[Solar System]], which is moving at velocity <math>v_{sun} </math> and the local cloud is moving at velocity <math>v_{L|C} </math>. Estimates of the number of protons range between 0.005 and 0.5&nbsp;cm<sup>−3</sup> resulting in a plasma mass density <math>9\times10^{-24}<\rho_{im}<3\times10^{-22}</math> kg/m<sup>3</sup>, which covers the range used by references in the magsail specific designs section. As summarized in the magsail specific design section, Gros cited references indicating that regions of the G-clouds may be colder and have a low ion density. A typical value assumed for approach to Alpha Centauri is a proton [[number density]] <math>n_{i}</math> of 0.1 protons per cm<sup>3</sup><ref name="Gry A58" /> corresponding to <math>\rho_{im}\approx 10^{-22}</math> kg/m<sup>3</sup>.

The spacecraft velocity <math>v_{sc}</math> is much greater than the ISM velocity at the beginning of a deceleration maneuver so the apparent plasma wind velocity from the spacecraft's viewpoint s approximately <math> u_{im} \approx - v_{sc} </math>.

Radio emissions of [[cyclotron radiation]] due to interaction of charged particles in the interstellar medium as they spiral around the magnetic field lines of a magnetic sail would have a frequency of approximately <math>120 \, v_{sc}/c</math> kHz.<ref>{{Cite journal |last=Zubrin |first=Robert |date=1994-07-01 |title=Detection of Extraterrestrial Civilizations via the Spectral Signature of Advanced Interstellar Spacecraft |url=https://aip.scitation.org/doi/abs/10.1063/1.2950156 |journal=AIP Conference Proceedings |volume=301 |issue=1 |pages=1407–1413 |doi=10.1063/1.2950156 |bibcode=1994AIPC..301.1407Z |issn=0094-243X}}</ref> The Earth's ionosphere would prevent detection on the surface, but a space-based antenna could detect such emissions up to several thousands of light years away.  Detection of such radiation could indicate activity of advanced extraterrestrial civilizations.

=== In a planetary ionosphere ===
A spacecraft approaching a planet with a significant upper atmosphere such as Saturn or Neptune could use a magnetic sail to decelerate by ionizing neutral atoms such that it behaves as a [[Plasma beta#Astrophysics|low beta plasma]].<ref name=":7" /><ref name=":36" /> The plasma mass in a planetary ionosphere (pi) <math>\rho_{pi} </math> is composed of multiple ion types and varies by altitude. The spacecraft velocity <math>v_{sc}</math> is much greater than the planetary ionosphere velocity in a deceleration maneuver so the apparent plasma wind velocity is approximately <math>u_{pi} \approx - v_{sc} </math> at the beginning of a deceleration maneuver.

=== In a planetary magnetosphere ===
Inside or near a planetary [[magnetosphere]], a magnetic sail can thrust against or be attracted to a planet's [[magnetic field]] created by a [[Dynamo theory|dynamo]], especially in an [[orbit]] that passes over the planet's magnetic poles.<ref name=":5">{{Cite journal |last=Zubrin |first=Robert |date=1991-06-24 |title=The use of magnetic sails to escape from low earth orbit |url=https://www.researchgate.net/publication/234453772 |journal=27th Joint Propulsion Conference |language=en |location=Sacramento, CA |publisher=American Institute of Aeronautics and Astronautics |doi=10.2514/6.1991-3352}}</ref> When the magnetic sail and planet's magnetic field are in opposite directions an attractive force occurs and when the fields are in the same direction a repulsive force occurs, which is not stable and means to prevent the sail from flipping over is necessary.

The thrust that a magnetic sail delivers within a magnetosphere decreases with the fourth power of its distance from the planet's internal magnetic field. When close to a planet with a strong [[magnetosphere]] such as [[Earth]] or a [[gas giant]], the magnetic sail could generate more thrust by interacting with the magnetosphere instead of the solar wind. When operating near a planetary or stellar magnetosphere the effect of that magnetic field must be considered if it is on the same order as the gravitational field.

By varying the magnetic sail's field strength and orientation a "[[perigee]] kick" can be achieved raising the altitude of the orbit's [[apogee]] higher and higher, until the magnetic sail is able to leave the planetary magnetosphere and catch the solar wind. The same process in reverse can be used to lower or circularize the apogee of a magsail's orbit when it arrives at a destination planet with a magnetic field.

In theory, it is possible for a magnetic sail to launch directly from the surface of a planet near one of its magnetic poles, repelling itself from the planet's magnetic field. However, this requires the magnetic sail to be maintained in an "unstable" orientation. Furthermore, the magnetic sail must have extraordinarily strong magnetic fields for a launch from Earth, requiring superconductors supporting 80 times the current density of the best known high-temperature superconductors as of 1991.<ref name=":5" />

In 2022 a spaceflight trial dubbed Jupiter Observing Velocity Experiment (JOVE) proposed using a [[plasma magnet]] to decelerate against the magnetosphere of Jupiter.<ref name=":11" />