Magnetic sail

thumb|upright=2.0|Magnetic sail animation

A magnetic sail is a proposed method of spacecraft propulsion where an onboard magnetic field source interacts with a plasma wind (e.g., the solar wind) to form an artificial magnetosphere (similar to Earth's magnetosphere) that acts as a sail, transferring force from the wind to the spacecraft requiring little to no propellant as detailed for each proposed magnetic sail design in this article.

The animation and the following text summarize the magnetic sail physical principles involved. The spacecraft's magnetic field source, represented by the purple dot, generates a magnetic field, shown as expanding black circles. Under conditions summarized in the overview section, this field creates a magnetosphere whose leading edge is a magnetopause and a bow shock composed of charged particles captured from the wind by the magnetic field, as shown in blue, which deflects subsequent charged particles from the plasma wind coming from the left.

Specific attributes of the artificial magnetosphere around the spacecraft for a specific design significantly affect performance as summarized in the overview section. A magnetohydrodynamic model (verified by computer simulations and laboratory experiments) predicts that the interaction of the artificial magnetosphere with the oncoming plasma wind creates an effective sail blocking area that transfers force as shown by a sequence of labeled arrows from the plasma wind, to the spacecraft's magnetic field, to the spacecraft's field source, which accelerates the spacecraft in the same direction as the plasma wind. dubbed the magsail, has the significant advantage of requiring no propellant and is thus a form of field propulsion that can operate indefinitely. A drawback of the magsail design was that it required a large (50–100 km radius) superconducting loop carrying large currents with a mass on the order of . The magsail design also described modes of operation for interplanetary transfers, thrusting against a planetary ionosphere or magnetosphere, In 2015, Freeland validated most of the initial magsail analysis, but determined that thrust predictions were optimistic by a factor of 3.1 due to a numerical integration error.

Subsequent designs proposed and analyzed means to significantly reduce mass. These designs require little to modest amounts of exhausted propellant and can thrust for years. All proposed designs describe thrust from solar wind outwards from the Sun. In 2000, Winglee and Slough proposed a Mini-Magnetospheric Plasma Propulsion (M2P2) design that injected low energy plasma into a much smaller coil with much lower mass that required low power. Simulations predicted impressive performance relative to mass and required power; however, a number of critiques raised issues: that the assumed magnetic field falloff rate was optimistic and that thrust was dramatically overestimated.

Starting in 2003, Funaki and others published a series of theoretical, simulation and experimental investigations at JAXA in collaboration with Japanese universities addressing some of the issues from criticisms of M2P2 and named their approach the MagnetoPlasma Sail (MPS). and 2014. Investigations and experiments continued reporting increased thrust experimentally and numerically considering use of a Magnetoplasmadynamic thruster (aka MPD Arc jet in Japan) in 2015, multiple antenna coils in 2019, and a multi-pole MPD thruster in 2020.

Slough published in 2004 and 2006 a method to generate the static magnetic dipole for a magnetic sail in a design called the Plasma magnet (PM) that was described as an AC induction motor turned inside out. A pair of small perpendicularly oriented coils acted as the stator powered by an alternating current to generate a rotating magnetic field (RMF) that analysis predicted and laboratory experiments demonstrated that a current disc formed as the rotor outside the stator. The current disk formed from electrons captured from the plasma wind, therefore requiring little to no plasma injection. Predictions of substantial improvements in terms of reduced coil size (and hence mass) and markedly lower power requirements for significant thrust hypothesized the same optimistic magnetic field falloff rate as assumed for M2P2. In 2022, a spaceflight trial dubbed Jupiter Observing Velocity Experiment (JOVE) proposed using a plasma magnet based sail for a spacecraft named Wind Rider using the solar wind to accelerate away from a point near Earth and decelerate against the magnetosphere of Jupiter.

A 2012, study by Kirtley and Slough investigated using the plasma magnet technology to use plasma in a planetary ionosphere as a braking mechanism and was called the Plasma Magnetoshell. This paper restated the magnetic field falloff rate to the value suggested in the critiques of M2P2 that dramatically reduces analytical predicted performance. Initial missions targeted deceleration in the ionosphere of Mars. Kelly and Little in 2019 A superconducting magsail coil augmented by an electron gun at the coil's center generates an electric field as in an electric sail that deflects positive ions in the plasma wind thereby providing additional thrust, which could reduce overall system mass.

Overview

thumb|upright

The Modes of operation section describes the important parameters of plasma particle density and wind velocity in conjunction with a use case for:

• Operation in a stellar (e.g., Sun) wind.
• Deceleration in the interstellar medium (ISM).
• Operation in a planetary ionosphere or planetary magnetosphere.

The Physical principles section details aspects of how charged particles in a plasma wind interact with a magnetic field and conditions that determine how much thrust force results on the spacecraft in terms of particle's behavior in a plasma wind, as well as the form and magnitude of the magnetic field related to conditions within the magnetosphere that differ for the proposed designs.

thumb

Charged particles such as electrons, protons and ions travel in straight lines in a vacuum in the absence of a magnetic field. As shown in the illustration in the presence of a magnetic field shown in green, charged particles gyrate in circular arcs with blue indicating positively charged particles (e.g., protons) and red indicating electrons. The particle's gyroradius is proportional to the ratio of the particle's momentum (product of mass and velocity) over the magnetic field. At 1 Astronomical Unit (AU), the distance from the Sun to the Earth, the gyroradius of a proton is ~72&nbsp;km and since a proton is ~1,836 times the mass of an electron, the gyroradius of an electron is ~40 m with the illustration not drawn to scale. For the magsail deceleration in the interstellar medium (ISM) mode of operation the velocity is a significant fraction of light speed, for example 5% c, 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 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/m³ (typically 10⁻²⁰ kg/m³).

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 and then rapidly decreases at 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), feasible uses of this involve maximum velocities below 10% c, taking decades to decelerate, for total travel times on the order of a century as described in the 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. --> 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 and the 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⁻³ resulting in a plasma mass density <math>9\times10^{-24}<\rho_{im}<3\times10^{-22}</math> kg/m³, 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 cm³ 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 low beta plasma. 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. and Funaki and Cruz.

Magnetohydrodynamic model

Magnetic sail designs operating in a plasma wind share a theoretical foundation based upon a magnetohydrodynamic (MHD) model, sometimes called a fluid model, from plasma physics for an artificially generated magnetosphere. Under certain conditions, the plasma wind and the magnetic sail are separated by a magnetopause that blocks the charged particles, which creates a drag force that transfers (at least some) momentum to the magnetic sail, which then applies thrust to the attached spacecraft as described in Andrews/Zubrin, Cattell, Funaki, An average plasma mass density per unit volume for charged particles in a plasma environment <math>pe</math> (<math>sw</math> for stellar wind, <math>pi</math> for planetary ionosphere, <math>im</math> for interstellar medium) is expressed in equation form from magnetohydrodynamics as<math>\textstyle \rho_{pe} = n_e m_e + \sum_{i}n_i m_i</math>. Note that this definition includes the mass of neutrons in an ion's nucleus. In SI Units per unit volume is cubic metre (m⁻³), mass is kilogram (kg), and mass density is kilogram per cubic metre (kg/m³).

thumb|upright=1.5|Artificial Magnetosphere Model of Basic Magnetic Sail

The figure depicts the MHD model as described in Funaki which states that the standoff distance <math>L</math> must be significantly greater than the ion gyroradius, also called the Larmor radius Thrust force derives from the momentum change of the solar wind, pressure by the solar wind on the magnetopause from equation and Lorentz force from currents induced in the magnetosphere interacting with the field source. The results quantified the coefficient of drag, steering (i.e., thrust direction) angle with the solar wind, and torque generated as a function of attack angle (i.e., orientation) The figure illustrates how the attack (or coil tilt) angle <math>\alpha _t</math> orientation of the coil creates a steering angle for the thrust vector and also torque imparted to the coil. Also shown is the vector for the interplanetary magnetic field (IMF), which at 1 AU varies with waves and other disturbances in the solar wind, known as space weather, and can significantly increase or decrease the thrust of a magnetic sail.

For a coil with radial orientation (like a Frisbee) the attack angle <math>\alpha _t</math>= 0° and with axial orientation (like a parachute) <math>\alpha _t</math>=90°. The Nishida 2005 results that covered two cases where MHD applicability occurs with <math>r_g/L</math>=1.125 and where a kinematic model is applicable <math>r_g/L</math>=0.125 to compute a coefficient of drag <math>C_d</math> and steering angle. As shown in Figure 4 of that paper when MHD applicability occurs the results are similar in form to Nishida 2005 for a coefficient of drag <math>C_D</math>, coefficient of lift <math>C_L</math> and a coefficient of moment <math>C_M</math> for a coil radius of <math>R_c</math>=100&nbsp;km and magnetopause radius <math>R_{mp}</math>=500&nbsp;km at 1 AU.

Magnetic field model

In a design, either the magnetic field source strength or the magnetopause radius <math>R_{mp}\approx L</math> the characteristic length must be chosen. A good approximation from Cattell Although a good fit for these parameters, the curve fit range of this model does not cover some relevant examples. Additional simulation results from Hajiwara15 are shown for the MHD and kinematic model as single data points as indicated in the legend. These models are all in close agreement. The kinematic models predict less force than predicted by the MHD model. In other words, the fraction <math>T_{loss}</math> of thrust force predicted by the MHD model is lost when <math>r_g/L<1</math> as plotted on the right axis. The solid blue and red lines show <math>T_{loss}</math> for Fujita04 Andrews asked Zubrin to help compute the magnetic scoop drag against the interplanetary medium, which turned out to be much greater than the ion drive thrust. The ion drive component of the system was dropped, and use of the concept of using the magnetic scoop as a magnetic sail or Magsail (MS) was born.thumb|upright=1.5|Andrews & Zubrin Magsail

The figure shows the magsail design

At a distance far from the loop center the magnetic field is approximately that produced by a magnetic dipole. The pressure at the magnetospheric boundary is doubled due to compression of the magnetic field and stated by the following equation at a point along the center-line axis or the target magnetopause standoff distance <math>L_Z</math>. as follows:

where <math>J_e</math> is the superconductor critical current density (A/m²) and <math display="inline">\delta_c</math> is the coil material density, for example <math>J_e</math> = 1&times;10¹¹ A/m² and <math display="inline">\delta_c</math> = 6,500&nbsp;kg/m³ for a superconductor in Freeland If operated in interstellar space low temperature superconductors (LTS) could be adequate since the temperature of a vacuum is 2.7Kelvins (K), but radiation and other heat sources from the spacecraft may render LTS impractical. The critical current <math>I_{cc}</math> of the HTS YBCO coated superconductor wire increases at lower temperatures with a current density <math>J_e</math> of 6&times;10¹⁰ A/m² at 77K and 9&times;10¹¹ A/m² at 5K.

Magsail kinematic model (MKM)

The MHD applicability test of equation fails in some ISM deceleration cases and a kinematic model is necessary, such as the one documented in 2017 by Claudius Gros summarized here. A spacecraft with an overall mass <math>m_{tot}</math> and velocity <math>v</math> follows that corroborated the above formula with parameters selected for the solar wind and reported a force no more than 9% less than the Gros model for <math>I</math>=10⁵ A and <math>R_c</math>=100 m with the coil in an axial orientation.. That analysis also reported on the effect of magsail tilt angle on lift and side forces for a use case in maneuvering within the solar system.

For comparison purposes, the effective sail area determined for the magsail by Zubrin from equation with the 3.1 correction factor from Freeland applied and using the same velocity value (resolving the discrepancy noted by Gros) as follows:

thumb|upright=1.5|Magsail MHD and kinematic model effective sail area

The figure shows the normalized effective sail area normalized by the coil area <math>\pi R_c^2</math> for the MKM case from Gros of equation and for Zubrin from equation for <math>I \approx I_G</math>, <math>R_c</math>=100&nbsp;km, and <math>n_p</math>=0.1&nbsp;cm⁻³ for the G-cloud on approach to Alpha Centauri corresponding to ISM density <math>\rho_{im}=1.67\times10^{-22}</math> kg/m³ consistent with that from Freeland The Freeland study predicted deceleration from 5% of light speed in approximately 19 years. The coil parameters <math>J_e</math>=10¹¹ A/m², <math>r_{sc}</math>= 5&nbsp;mm, <math>\rho_{sc}</math>=6,500&nbsp;kg/m³, resulted in an estimated coil mass of <math>M_c(phy)</math>=1,232 tonnes. Although the critical current density <math>J_e</math> was based upon a 2000 Zubrin NIAC report projecting values through 2020, the assumed value is close to that for commercially produced YBCO coated superconductor wire in 2020. The mass estimate may be optimistic since it assumed that the entire coil carrying mass is superconducting while 2020 manufacturing techniques place a thin film on a non-superconducting substrate. For the interstellar medium plasma density <math>\rho_{im}</math>=1.67&times;10⁻²² with an apparent wind velocity 5% of light speed, the ion gyroradius is 570&nbsp;km and thus the design value for <math display="inline">R_{mp}</math> meets the MHD applicability test of equation . Equation gives the required coil current as <math>I_c</math>~7,800 kA and from equation <math>M_c(min)</math>= 338 tonnes; however, but the corresponding superconducting wire minimum radius from equation is <math>r_c(min) </math> =1&nbsp;mm, which would be insufficient to handle the decelerating thrust force of <math>F_{MS}</math> ~ 100,000 N predicted by equation and hence the design specified <math>r_{sc}</math>= 5&nbsp;mm to meet structural requirements. In a complete design, the mass of infrastructure, including coil shielding to maintain critical temperature and survive abrasion in outer space, must also be included. Appendix A estimates these as 90 tonnes for wire shielding and 50 tonnes for the spools and other magsail infrastructure. Freeland compared this magsail deceleration design with one where both acceleration and deceleration were performed by a fusion engine and reported that the mass of such a "dirty Icarus" design was over twice that of a magsail used for deceleration. <!-- Cite Crowl analysis of Fusion versus magsail for deceleration? -->An Icarus design published in 2020 used a Z-pinch fusion drive in an approach called Firefly that dramatically reduced mass of the fusion drive and made fusion only drive performance for acceleration and deceleration comparable to the fusion for acceleration and magsail for deceleration design.<!-- Need to confirm that a source states this: "although it could be used to decelerate in other directions, such as on approach to a star". Magsail Freeland describes detaching magsail and using fusion for such deceleration. -->

In 2017, Gros and about 0.005&nbsp;cm⁻³ (9&times;10⁻²³ kg/m³) for voids of the local bubble. Patches of cold interstellar clouds with less than 200 AU may have large densities of neutral hydrogen up to 3000&nbsp;cm⁻³, which would not respond to a magnetic field. For a high speed mission to Alpha Centauri with initial velocity before deceleration <math>v_0=c/10</math> using a coil mass of 1500 tons and a coil radius of <math>R</math>=1600&nbsp;km, the estimated stopping distance <math>x_{max}</math> was 0.37 light years and the total travel time of 58 years with 1/3 of that being deceleration.

In 2017, Crowl documented a design for a mission starting near the Sun and destined for Planet nine approximately 1,000 AU distant used Kajimura 2012 simulation results used the Quarta "thick" magnetopause model and predicted a Venus to Earth transfer orbit of approximately 8 years for a coil radius of <math>R_c</math>~1&nbsp;km. with characteristic acceleration <math>a_c</math>=0.1&nbsp;mm/s². In 2020 Perakis

• To travel out of the solar system
• To travel between the planets for low power requirements of ~1&nbsp;kW per 100&nbsp;kg of payload and ~0.5&nbsp;kg fuel consumption per day for acceleration periods of several days to a few weeks.

The figure based upon Winglee, Arita, and Funaki wave that injects plasma fed from a source into a coil of radius <math display="inline">R_c</math> that carries a current of <math>I_c</math>, which generates a magnetic field. The excited injected plasma enhances the magnetic field and generates a miniature magnetosphere around the spacecraft, analogous to the heliopause where the Sun injected plasma encounters the interstellar medium, coronal mass ejections or the Earth's magnetotail. The injected plasma created an environment that analysis and simulations showed had a magnetic field with a falloff rate of <math>1/r</math> as compared with the classical model of a <math display="inline">1/r^3</math> falloff rate, making the much smaller coil significantly more effective based upon analysis and simulation. Their comments also indicated that the magnetic field lines may not close near enough to the coil to achieve significant transfer of force. Their analysis made an analogy to the Heliospheric current sheet as an example in astrophysics where the magnetic field could falloff at a rate of between <math display="inline">1/r</math> and <math display="inline">1/r^2</math>. They also analyzed current sheets reported by Winglee from the magnetopause to the spacecraft in the windward direction and a current sheet in the magnetotail. Their analysis indicated that the current sheets needed to pass extremely close to the spacecraft to impart significant force could generate significant heat and render this leverage impractical.

In 2005, Cattell and others The accompanying presentation has some good animations that illustrate physical principles described in the report. A 2004 Winglee paper focused on usage of M2P2 for electromagnetic shielding. Beginning in 2003, the Magneto plasma sail design further investigated the plasma injection augmentation of the magnetic field, used larger coils Simulation results indicated a significant increase in magnetosphere size with plasma injection as compared to the Magsail design, which had no plasma injection. Analysis showed how adjustment of the MPS steering angle created force that could reach the outer planets. A satellite trial was proposed. Preliminary performance results were reported but later modified in subsequent papers.

Many MPS papers have been published on the magnetic sail contributing to the understanding of general physical principles of an artificial magnetosphere, its magnetohydrodynamic model, and the design approach for computing the magnetopause distance for a given magnetic field source are documented in the linked sections of this article.

In 2004 Funaki and others analyzed MPS cases where <math>R_c</math>=10 m and <math>R_c</math>=100 m

An analogy with the Earth's magnetosphere and magnetopause in determining the penetration of plasma irregularities into the magnetopause defines the key parameter of a local kinetic plasma beta as the ratio of the dynamic pressure <math>p_{dyn}</math> of the injected plasma over the magnetic pressure <math>p_{dyn}</math> as follows

In 2005 Funaki and others published numerical analysis showing <math>f_0</math>=1.88 for <math>\beta_k</math>=0.1. In 2009 Kajimura published simulation results with <math>\beta_k</math>=5 and <math>\beta_i</math> ranging from 6 to 20 that the magnetic field falloff rate <math>f_0</math> with argon and xenon plasma injected into the polar region was <math>f_0</math>=2.1 and with argon plasma injected into the equatorial region was <math>f_0</math>=1.8.

If <math>\beta_k>1</math> then the Injection of a high-velocity, high-density plasma into a magnetosphere as proposed in M2P2 freezes the motion of a magnetic field into the plasma flow and was believed to inflate the magnetosphere. published simulation and theoretical results regarding how characteristics of the injected plasma affected thrust gain through creation of an equatorial ring current. They defined thrust gain for MPS as <math>G_{MPS}=F_{MPS}/F_{mag}</math>: the ratio of the force generated by low beta plasma injection <math>F_{MPS}</math> divided by that of a pure magnetic sail <math>F_{mag}</math> from equation with <math display="inline">f_o =3</math> and <math>C_{SO}=0.5</math> for <math>r_g\leq L</math> or from equation for <math>r_g>L</math>. They reported <math>G_{MPS}</math> of approximately 40 for magnetospheres less than the MHD applicability test and 3.77 for a larger magnetosphere where MHD applicability occurred, larger than values reported in 2012 of 20 and 3.3, respectively. Simulations revealed that optimum thrust gain occurred for <math>\beta_k<1</math> and <math>\beta_i \approx 10</math>.

In 2014 Arita, Nishida and Funaki published simulation results Equation (12) of their study included the additional force of the injected plasma jet <math>F_{jet}</math> consisting of momentum and static pressure of ions and electrons and defined thrust gain as <math display="inline">F_{MPS}/(F_{mag}+F_{jet})</math>, which differs from the definition of a term by the same name in other studies. Simulation results require significant compute time, for example it took 1024 CPUs 4 days to simulate the simplest case and 4096 CPUs one week to simulate a more complex case. The MHD applicability test of equation for the solar wind is <math>L \approx</math>72&nbsp;km. Therefore, the estimated force of the MPS is that of equation multiplied by the empirically determined thrust gain <math>G_{MPS}</math> from the figure multiplied by the percentage thrust loss <math>T_{loss}</math> from equation

For example, using solar wind parameters <math>\rho</math>=8&times;10⁻²¹ kg/m³ and <math>u</math>=500&nbsp;km/s then <math>r_g</math>=72&nbsp;km and <math>B_{mp}</math>=4&times;10⁻⁸ T. With <math>L</math>=10⁵ m for <math>f_o</math>=3 then <math>r_g < L</math> and <math>T_{loss}\approx</math> 11% from equation . The magnetic field only force with a coil radius of <math>R_c</math>=6,300 m and coil current <math>I_c</math>=1.6&times;10⁶ A yields <math>B_0</math>=1.6&times;10⁻⁴ T from equation and with <math>C_d</math>=5 the magnetic force only is 175 N from equation . Determining <math>G_{MPS} \approx</math>4 from the figure at <math>L</math>=10⁵ m as the multiplier for the magnetic-only force then the MPS force <math>F_{MPS} \approx</math>700 N.

Since MPS injects ionized gas at a rate of <math>m_{in}</math> that can be viewed as a propellant it has a specific impulse <math>I_{sp}=F_{MPS}/m_{in}/g_0</math> where <math>g_0</math> is the acceleration of Earth's gravity. Funaki In 2020 Murayama and others published additional experimental results for a multi-pole MPD thruster.

In 2020 Peng and others published MHD simulation results for a magnetic dipole with plasma injection operating in Low Earth orbit at 500&nbsp;km within the Earth's Ionosphere where the ion number density is approximately 10¹¹ m⁻³. As reported in Figure 3, the magnetic field strength initially falls off as 1/r and then approaches 1/r² at larger distances from the dipole. The radius of the artificial mini-magnetosphere could extend up to 200 m for this scenario. They reported that the injected plasma reduced magnetic field fall off rate and created of a drift current, similar to earlier reported MPS results for the solar wind. The induced current disc carries a direct current <math>I_{cd}</math> orders of magnitude larger than the input alternating current <math>I_c</math> and forms a static dipole magnetic field oriented perpendicular to the current disc reaching a standoff balance with the plasma wind pressure at distance <math>R_{mp} \approx L</math> at the magnetopause boundary according to the MHD model of an artificial magnetosphere.

The magnetic field falloff rate was assumed in 2001 and Kirtley and Slough in a 2012 NIAC report<!-- DM: Confirm correct units for Spitzer resistivity. --> of the plasma of ~1.2&times;10⁻³ <math>T_e^{-3/2}</math> where <math>T_e</math> is the electron temperature assumed to be 15 eV, In 2019 Kelly and Little published simulation results for magnetoshell performance scaling. A magnet with radius <math>R_c</math>=1 m was tethered to a spacecraft with batteries for 1,000 seconds of operation (longer than aerocapture designs). The simulations assumed a magnet mass <math>M_c</math>=1,000&nbsp;kg and total magnetoshell system mass of 1,623&nbsp;kg, suitable for a Cassini–Huygens or Juno size orbiter. The planet's mass and atmosphere atomic composition and density determine a threshold velocity where magnetoshell operation is feasible. Saturn and Neptune have a hydrogen atmosphere and a threshold velocity of approximately 22&nbsp;km/s. In a Neptune mission a <math>\Delta v</math>=6&nbsp;km is required for a 5,000&nbsp;kg spacecraft and must average 50&nbsp;kN for the maneuver duration. The model overestimates performance for N₂ (Earth, Titan) and CO₂ (Venus, Mars) atmospheres since multiple ion species are created and more complex interactions occur. Furthermore, the relatively lower mass of Venus and Mars reduces the threshold velocity below that of feasible magnetoshell operation. The paper states that aerocapture technologies are mature enough for these mission profiles.

In 2021, Kelly and Little published further details for use of drag-modulated plasma aerocapture (DMPA) that when compared to Adaptable Deployable Entry and Placement Technology (ADEPT) for drag-modulated aerocapture (DMA) to Neptune that could deliver 70% higher orbiter mass and experience 30% lower stagnation heating.

Beam powered magsail (BPM)

A beam-powered of M2P2 variant, MagBeam was proposed in 2011. In this design a magnetic sail is used with beam-powered propulsion, by using a high-power particle accelerator to fire a beam of charged particles at the spacecraft. The magsail would deflect this beam, transferring momentum to the vehicle, that could provide higher acceleration than a solar sail driven by a laser, but a charged particle beam would disperse in a shorter distance than a laser due to the electrostatic repulsion of its component particles. This dispersion problem could potentially be resolved by accelerating a stream of sails which then in turn transfer their momentum to a magsail vehicle, as proposed by Jordin Kare.

Performance comparison

The table below compares performance measures for the magnetic sail designs with the following parameters for the solar wind (sw) at 1 AU: velocity <math>u_{sw}</math>= 500&nbsp;km/s, number density <math>n_i</math>= 5&times;10⁶ m⁻³, ion mass <math>m_i</math> = 1.67&times;10⁻²⁷ kg a proton mass, resulting in mass density <math>\rho_{sw}= m_i n_i</math> = 8.4&times;10⁻²¹ kg/m³, and coefficient of drag <math>C_d</math>=5 where applicable. Equation gives the magnetic field at magnetopause as <math>B_{mp}</math>≈ 36 nT, equation gives the ion gyroradius <math>r_g </math>≈ 72&nbsp;km for <math>C_{Li}</math>=2. Table entries in boldface are from a cited source as described in the following:

Equation determines force for the Magsail (MS) divided by the Freeland correction factor 3.1, The paper highlighted technology challenges in terms of the magnetic field source, energy required and interaction between the solar wind and the spacecraft's magnetic field, summarizing that these issues were not insurmountable. The major unresolved issue is spacecraft and mission design that account for the potentially highly variable solar wind velocity and plasma density that could complicate maneuvers by a spacecraft employing magnetic sail technology. Some means of modulating thrust is necessary. If the mission objective is to rapidly escape the solar system then the paper states that this is less of an issue.

In 2006, Bolonkin published a paper that questioned the theoretical viability of a Magsail and described common mistakes. Equation (2) states that the magnetic field of electrons rotating in the large coil was greater than and opposed the magnetic field generated by the current in the coil and hence no thrust would result. In 2014 Vulpetti published a rebuttal that summarized plasma properties, in particular the fact that plasma is quasi-neutral