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.

These concepts apply to all proposed magnetic sail system designs, with the difference how the design generates the magnetic field and how efficiently the field source creates the artificial magnetosphere described above. The History of concept section summarizes key aspects of the proposed designs and relationships between them as background. The cited references are technical with many equations and in order to make the information more accessible, this article first describes in text (and illustrations where available) beginning in the overview section and prior to each design, section or groups of equations and plots intended for the technically oriented reader. The beginning of each proposed design section also contains a summary of the important aspects so that a reader can skip the equations for that design. The differences in the designs determine performance measures, such as the mass of the field source and necessary power, which in turn determine force, mass and hence acceleration and velocity that enable a performance comparison between magnetic sail designs at the end of this article. A comparison with other spacecraft propulsion methods includes some magnetic sail designs where the reader can click on the column headers to compare magnetic sail performance with other propulsion methods. The following observations result from this comparison: magnetic sail designs have insufficient thrust to launch from Earth, thrust (drag) for deceleration for the magsail in the interstellar medium is relatively large, and both the magsail and magnetoplasma sail have significant thrust for travel away from Earth using the force from the solar wind.

History of concept

An overview of many of the magnetic sail proposed designs with illustrations from the references was published in 2018 by Djojodihardjo. The earliest method proposed by Andrews and Zubrin in 1988, dubbed the magsail, has the significant advantage of requiring no propellant and is thus a form of propellantless propulsion that can operate indefinitely. A drawback of the magsail design was that it required a large (50–100km 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, escape from low Earth orbit as well as deceleration of an interstellar craft over decades after being initially accelerated by other means, for example. a fusion rocket, to a significant fraction of light speed, with a more detailed design published in 2000. 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). In 2011, Funaki and Yamakawa authored a chapter in a book that is a good reference for magnetic sail theory and concepts. MPS research resulted in many published papers that advanced the understanding of physical principles for magnetic sails. Best performance occurred when the injected plasma had a lower density and velocity than considered in M2P2. Thrust gain was computed as compared with performance with a magnetic field only in 2013 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 published simulation results using a multi-turn coil and not the plasma magnet showed that the magnetoshell was viable for orbital insertion around Mars, Jupiter, Neptune and Uranus and in 2021 showed that it was more efficient than aerocapture for Neptune.

In 2021, Zhenyu Yang and others published an analysis, numerical calculations and experimental verification for a propulsion system that was a combination of the magnetic sail and the electric sail called an electromagnetic sail. 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

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. 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 ~72km 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, the gyroradius is ~ 500km for protons and ~280 m for electrons. When the magsail magnetopause radius is much less than the proton gyroradius the magsail kinematic model by Gros in 2017, which considered only protons, predicts a marked reduction in thrust force for initial ship velocity greater than 10% c prior to deceleration. When the magnetosphere radius is much greater than the spacecraft's magnetic field source radius, all proposed designs, except for the magsail, use a magnetic dipole approximation for an Amperian loop shown in the center of the illustration with the X indicating current flowing into the page and the dot indicating current flowing out of the page. The illustration shows the resulting magnetic field lines and their direction, where the closer spacing of lines indicates a stronger field. Since the magsail uses a large superconducting coil that has a radius on the same order as the magnetosphere the details of that design use the magsail MHD model employing the Biot–Savart law that predicts stronger magnetic fields near and inside the coil than the dipole model. A Lorentz force occurs only for the portion of a charged particle's velocity at a right angle to the magnetic field lines and this constitutes the magnetic force depicted in the summary animation. Electrically neutral particles, such as neutrons, atoms and molecules are unaffected by a magnetic field.

A condition for applicability of magnetohydrodynamic (MHD) theory, which models charged particles as fluid flows, is that to achieve maximum force the radius of the artificial magnetosphere be on the same order as the ion gyroradius for the plasma environment for a particular mode of operation is the falloff rate. Classic magnetic dipole=1 that as shown in numerical examples summarized at the end of the corresponding design sections predicted a very large performance gain. Several researchers independently created a magnetic field model=2 falloff rate was the best achievable. In 2011 the plasma magnet author from 1 to 2 and that is the value used for the plasma magnet for performance comparison in this article. The magnetoplasma sail (MPS) between 1.5 and 2. has a significant impact on performance or the mode of operation accelerating away from the Sun where the mass density of ions in the plasma decreases according to an Inverse-square law with distance from the Sun (e.g., AU) increases. The illustration shows in a semi-log plot on relative force F from Equation =1 is stated in several plasma magnet references, for example Slough and Freeze on force, and therefore acceleration, becomes grerater as distance from the Sun increases.

At scales where the artificial magnetospheric object radius is much less than the ion gyroradius but greater than the electron gyroradius, the realized force is markedly reduced and electrons create force in proportion much greater than their relative mass with respect to ions as detailed in the General kinematic model section where researchers report results from a compute intensive method that simulates individual particle interactions with the magnetic field source.

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 and from the spacecraft point of view the apparent wind.

Plasma mass density and velocity terminology and units

A 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 section.

(positive meaning acceleration in the same direction as the wind and negative meaning deceleration opposite the wind direction) for a particular plasma environment (pe.

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. dynamically ranges from 250 to 750km/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 kg/m3 (typically 10−20 kg/m3).

decreases according to an Inverse-square law with the distance from the Sun as stated by Andrews/Zubrin and Borgazzi. The velocity for values near the Sun is nearly constant, falling off slowly after 1 AU 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. ) Centauri, which as shown in the figure is separated by the local bubble and the G-clouds and the Solar System. Estimates of the number of protons range between 0.005 and 0.5cm−3 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 of 0.1 protons per cm3 kg/m3.

.

Radio emissions of cyclotron radiation kHz. 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. 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, especially in an orbit that passes over the planet's magnetic poles. 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.

In 2022 a spaceflight trial dubbed Jupiter Observing Velocity Experiment (JOVE) proposed using a plasma magnet to decelerate against the magnetosphere of Jupiter.

Physical principles

Physical principles involved include: interaction of magnetic fields with moving charged particles; an artificial magnetosphere model analogous to the Earth's magnetosphere, MHD and kinematic mathematical models for interaction of an artificial magnetosphere with a plasma flow characterized by mass and number density and velocity, and performance measures; such as, force achieved, energy requirements and the mass of the magnetic sail system.

Magnetic field interaction with charged particles

An ion or electron with charge in a plasma moving at velocity in a magnetic field and electric field is treated as an idealized point charge in the Lorentz force. This means that the force on an ion or electron is proportional to the product of their charge perpendicular to the magnetic field flux density , in SI units as teslas (T). A magnetic sail design introduces a magnetic field into a plasma flow which under certain conditions deflects the electrons and ions from their original trajectory with the particle's momentum transferred to the sail and hence the spacecraft thereby creating thrust. An electric sail uses an electric field that under certain conditions interact with charged particles to create thrust.

Artificial magnetospheric model

The characteristics of the Earth's magnetosphere have been widely studied as a basis for magnetic sails. The figure shows streamlines of charged particles from a plasma wind from the Sun (or a star) or an effective wind when decelerating in the ISM flowing from left to right. A source attached to a spacecraft generates a magnetic field. Under certain conditions at the boundary where magnetic pressure equals the plasma wind kinetic pressure an artificial bow shock and magnetopause from the field source. The ionized plasma wind particles create a current sheet along the magnetopause, which compresses the magnetic field lines facing the oncoming plasma wind by a factor of 2 at magnetopause as shown in Figure 2a. The magnetopause deflects charged particles, which affects their streamlines and increases the density at magnetopause. A magnetospheric bubble or cavity forms that has very low density downstream from the magnetopause. Upstream from the magnetopause a bow shock develops. Simulation results often show the particle density through use of color with an example shown in the legend in the lower left. This figure uses aspects of the general structure from Zubrin, Toivanen and Funaki and aspects of the plasma density from Khazanov 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, and Toivanen.

A plasma environment has fundamental parameters, and if a cited reference uses cgs units these should be converted to SI units as defined in the NRL plasma formulary, which this article uses as a reference for plasma parameter units not defined in SI units per unit volume each with electron mass. for interstellar medium) is expressed in equation form from magnetohydrodynamics. 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). The figure depicts the MHD model as described in Funaki and Djojodihardjo.. The spacecraft and field source generate a magnetic field on the right side.

with SI units of Pascal (Pa, or N/m2) as follows:

is the plasma mass density for a specific plasma environment the magnetic field flux density at magnetopause, μ0 is the vacuum permeability (N A−2) modeled as dynamic pressure with no magnetic field compression, modeled as ram pressure with no magnetic field compression modeled as ram pressure with magnetic field compression by a factor of 2 Equation that satisfies the pressure balance at magnetopause standoff as:

The force with SI Units of Newtons (N) derived by a magnetic sail for a plasma environment is determined from MHD equations as reported by principal researchers Funaki, Slough, Andrews and Zubrin, and Toivanen as follows:

is a coefficient of drag determined by numerical analysis. Note that this equation has the same form as the drag equation in fluid dynamics is a function of coil attack angle on thrust and steering angle. The power (W) of the plasma wind is the product of velocity and a constant force

where equation was used to derive the right side.

MHD applicability test

As summarized in the overview section, an important condition for a magnetic sail to generate maximum force is that the magnetopause radius be on the order of an ion's radius of gyration. Through analysis, numerical calculation, simulation and experimentation an important condition for a magnetic sail to generate significant force is the MHD applicability test, must be significantly greater than the ion gyroradius, also called the Larmor radius or cyclotron radius:

where is the elementary charge. For example, in the solar wind with 5 ions/cm3 the proton mass (kg) = 400=0.5 from equation 72km. decreases meaning less thrust from the plasma wind transfers to the spacecraft and is instead lost to the plasma wind. In 2004, Fujita for a magnetic sail operating in the radial orientation resulting in the following approximate formula:.

Coil attack angle effect on thrust and steering angle

In 2005 Nishida and others published results from numerical analysis of an MHD model for interaction of the solar wind with a magnetic field of current flowing in a coil that momentum is indeed transferred to the magnetic field produced by field source and hence to the spacecraft. Thrust force derives from the momentum change of the solar wind, pressure by the solar wind on the magnetopause from equation 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.

=90°. The Nishida 2005 results=90°. A number of magnetic sail design and other papers cite these results. In 2012 Kajimura reported simulation results and steering angle. As shown in Figure 4 of that paper when MHD applicability occurs the results are similar in form to Nishida 2005 occurs with the coil in a radial orientation. The steering angle is positive when MHD is applicable and negative when a kinematic model applies. The 2012 Nishida and Funaki published simulation results=100=500km at 1 AU.

Magnetic field model

the characteristic length must be chosen. A good approximation from Cattell and Toivanen from the field source to magnetopause starts with the equation:

as follows:

is a constant multiplying the magnetic moment (A m2) =2 near the field source was used by Andrews and Zubrin.

The Amperian loop model is the current in amperes (A) into equation yields the following:

from the pressure balance analysis from equation yields the following:

and is the same form as the magnetopause distance of the Earth. Equation determined from the pressure balance equation . Substituting this into equation as follows:

using equation and equation and the right hand side from equation (20) specifically applied to M2P2 term. Note that force increases as falloff rate decreases. For the solar wind case, substituting into and using the function for the solar wind plasma mass density, the distance from the sun in Astronomical units (AU) results in the following expression: , the effective sail blocking area.

increases, resulting in constant force and hence constant acceleration inside the heliosphere.. The example in the overview at 1 AU. === General kinematic model ===

When the MHD applicability test. from equation 72km at 1 AU from equation . The dashed blue line plots the hybrid MHD/kinematic model from equation from Fujita04. The red dashed line plots a curve fit to simulation results from Ashida14. 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 for Fujita04 and Ashida18.

Performance measures

. The thrust to weight is also an important performance measure. Other limitations and constraints may be specific to a particular design. The M2P2 and MPS designs, as well as potentially the plasma magnet design, exhaust some plasma as part of inflating the magnetospheric bubble and these cases also have a specific impulse and effective exhaust velocity performance measure.

Proposed magnetic sail systems

This section contains a subsection for each of the proposed magnetic sail designs introduced in the summary. Each subsection begins with a high-level description of that design and an illustration. The cited references are technical and contain many equations, for which this article includes where applicable a common notation described in the Physical principles section, and in other cases the notation from a cited reference. The focus is to include equations used in the Performance comparison section. The subsections include plots of variables with relevant units related to this objective that are preceded by a summary description.

Magsail (MS)

Andrews was working on use of a magnetic scoop to gather interstellar material as propellant for a nuclear electric ion drive spacecraft, allowing the craft to operate in a similar manner to a Bussard ramjet, whose history goes back to at least 1973. 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. The figure shows the magsail design consisting of a loop of superconducting on the order of 100 that generates a magnetic field, which was modeled according to the Biot–Savart law inside the loop and as a magnetic dipole far outside the loop. With respect to the plasma wind direction a magsail may have a radial (or normal) orientation or an axial orientation that can be adjusted to provide torque for steering. In non-axial configurations lift is generated that can change the spacecraft's momentum. The loop connects via shroud lines (or tethers) to the spacecraft in the center. Because a loop carrying current is forced outwards towards a circular shape by its magnetic field, the sail could be deployed by unspooling the conductor wire and applying a current through it via the peripheral platforms. The loop must be adequately attached to the spacecraft in order to transfer momentum from the plasma wind and would pull the spacecraft behind it as shown in the axial configuration in the right side of the figure. This design has a significant advantage of requiring no propellant and is thus a form of propellantless propulsion that can operate indefinitely.

MHD model

Analysis of magsail performance was done using a simulation and a fluid (i.e., MHD) model with similar results observed for one case. The magnetic moment of a current loop (A m2) along the center-line axis perpendicular to the loop is derived from the Biot-Savart law as follows.

At a distance far from the loop center the magnetic field is approximately that produced by a magnetic dipole. from equation yields

for a tilt angle, but according to Freeland an error was made in numerical integration in choosing the ellipse downstream from the magnetopause instead of the ellipse upstream that made those results optimistic by a factor of approximately 3.1, which should be used to correct any drag(thrust) force results using Instead, this article uses the approximation for a spherical bubble that corrects this error and is close to the analytical formula for the axial configuration as the force for the Magsail as follows In 2004 Toivanen and Janhunen did further analysis on the Magsail that they called a Plasma Free MagnetoPause (PFMP) that produced similar results to that of Andrews and Zubrin.

Coil mass and current (CMC)

The minimum required mass to carry the current in equation or other magnetic sail designs from Andres/Zubrin (9) and Crowl as follows:

is the superconductor critical current density (A/m2) = 11011 A/m2 = 6,500kg/m3 for a superconductor in Freeland The physical mass of the coil is

= 10mm. in order for the coil to carry the superconductor critical current = 7,854 kiloampere (kA.)

Setting equation =0 equal to equation yields the minimum required coil radius

If operated within the solar system, high temperature superconducting wire (HTS) is necessary to make the magsail practical since required current is large, millions of amperes. Protection from solar heating is necessary closer to the Sun, for example by highly reflective coatings. If operated in interstellar space low temperature superconductors (LTS) could be adequate since the temperature of a vacuum is 2.7Kelvins (K) of the HTS YBCO coated superconductor wire of 61010 A/m2 at 77K and 91011 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. follows of motion as:

m−3 kg is the proton kg/m3 m2 is completed reflected. Note that this equation is of the same form as term as just a number.

by integrating the degree of reflection of approaching protons interacting with the superconducting loop magnetic field according to the Biot-Savart law. An accurate curve fit as reported in Figure 4 to the numerical evaluation for the effective reflection area for a magnetic sail in the axial configuration from equation (8) was

the speed of light=105 A, the current through the loop. In 2020, Perakis published an analysis=105=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:

for the MKM case from Gros of equation and for Zubrin from equation =100=0.1cm−3 for the G-cloud kg/m3 consistent with that from Freeland <1 from equation from the MHD applicability test 10% after which point the Zubrin magsail model of Equation becomes increasingly optimistic and equation (hence underestimating force), equation < 0.1%.

from equation m/s from kg as follows:

=0 the above equation is defined in in with numerical integration required to compute the time required to decelerate.. In 2017 Crowl. and time to decelerate. given a starting relative velocity m/s consistent with that from Freeland for the same parameters above. Equation of 100 tonnes using the same values used by Freeland = 1011 A/m2=6,500kg/m3 for the superconducting coil. Equation =4 for the Andrews/Zubrin model to align with equation definition of force from the Gros model. Acceleration is force divided by mass, velocity from for the same parameters closely tracks the numerical integration result.

Specific designs and mission profiles

Dana Andrews and Robert Zubrin first proposed the magnetic sail concept in 1988 for interstellar travel for acceleration by a fusion rocket, coasting and then deceleration via a magsail at the destination that could reduce flight times by 40–50 years In 1989 details for interplanetary travel were reported In 1990 Andrews and Zubrin reported on an example for solar wind parameters one AU m−3=500km/s the field strength required to resist the dynamic pressure of the solar wind is 50 nT from equation =100= reported a thrust of 1980 newtons and a coil mass of 500 tonnes. For the above parameters with the correction factor of 3.1 applied to equation yields the same thrust and equation yields the same coil mass. Results for another 4 solar wind cases were reported, but the MHD applicability test of equation fails in these cases.

In 2015, Freeland documented a use case with acceleration away from Earth by a fusion drive with a magsail used for interstellar deceleration on approach to Alpha Centaturi as part of a study to update Project Icarus=260 of 1,320 kg/m3, almost identical to the n(H I) measurement of 0.098cm−3 by Gry in 2014.=1011 A/m2= 5=6,500kg/m3 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=1.6710−22 with an apparent wind velocity 5% of light speed, the ion gyroradius is 570 meets the MHD applicability test of equation . Equation ~7,800 kA and from equation = 338 tonnes; however, but the corresponding superconducting wire minimum radius from equation =1 ~ 100,000 N predicted by equation = 5mm 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. 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.

In 2017, Gros reported numerical examples for the Magsail kinematic model that used different parameters and coil mass models than those used by Freeland. That paper assumed hydrogen ion (H I) number densities of 0.05-0.2cm−3 (910−23 - 310−22 kg/m3) for the warm local clouds and about 0.005cm−3 (910−23 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 3000cm−3, which would not respond to a magnetic field. For a high speed mission to Alpha Centauri=1600 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 that employed the Magsail kinematic model. The design accounted for the Sun's gravity as well as the impact of elevated temperature on the superconducting coil, composed of meta-stable metallic hydrogen, which has a mass density of 3,500kg/m3 about half that of other superconductors. The mission profile used the Magsail to accelerate away from 0.25 to 1.0 AU from the Sun and then used the Magsail to brake against the Local ISM on approach to Planet nine for a total travel time of 29 years. Parameters and coil mass models differ from those used by Freeland.

Another mission profile uses a magsail oriented at an attack angle to achieve heliocentric transfer between planets moving away from or toward the Sun. In 2013 Quarta and others used Kajimura 2012 simulation results~1=1mm/s2. In 2019 Bassetto and others~1=0.1mm/s2. In 2020 Perakis used the Magsail kinematic model=104 A and spacecraft mass of 600kg that changed attack angle to accelerate away from the Earth orbit and decelerate to Jupiter orbit within 20 years.

Mini-magnetospheric plasma propulsion (M2P2)

In 2000, Winglee, Slough and others proposed a design order to reduce the size and weight of a magnetic sail well below that of the magsail and named it mini-magnetospheric plasma propulsion (M2P2) that reported results adapted from a simulation model of the Earth's magnetosphere. The calculates speeds of 50 to 80km s−1 could enable spacecraft:

• To travel out of the solar system

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

The figure based upon Winglee, Hajiwara, Arita, and Funaki illustrates the M2P2 design, which was the basis of the subsequent Magneto plasma sail (MPS) design. Starting at the center with a solenoid=1,000 turns carrying a radio frequency current that generates a helicon, 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 falloff rate, making the much smaller coil significantly more effective based upon analysis and simulation. The pressure of the inflated plasma along with the stronger magnetic field pressure at a larger distance due to the lower falloff rate would stretch the magnetic field and more efficiently inflate a magnetospheric bubble around the spacecraft.

=2.5= 0.1 m, 6 orders of magnitude less than the magsail coil with correspondingly much lower mass. An estimate for the weight of the coil was 10kg and 40 1010−3 1 N. The magnetic-only sail force from equation =310−11 N and thus M2P2 reported a thrust gain of 41010 mass flow rate (kg/s) it is viewed as a propellant and therefore has a specific impulse (s) is the acceleration of Earth's gravity=0.5 is 173km/s for 1 N of thrust force. Winglee assumed total propellant mass of 30kg and therefore propellant would run out in 60 days.

In 2003, Khazanov published MagnetoHydroDynamic (MHD) and kinetic studies. The plasma density plots from Khazanov indicated a relatively high density inside the magnetospheric bubble as compared with the external solar wind region that differed significantly from those published by Winglee where the density inside the magnetospheric bubble was much less than outside in the external solar wind region.

A detailed analysis by Toivanen and others in 2004 compared a theoretical model of Magsail, dubbed Plasma-free Magnetospheric Propulsion (PFMP) versus M2P2 and concluded that the thrust force predicted by Winglee and others was over ten orders of magnitude optimistic since the majority of the solar wind momentum was delivered to the magnetotail and current leakages through the magnetopause and not to the spacecraft. 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. 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 magnetic field falloff rate was not possible.

The expansion of the magnetic field using injected plasma was demonstrated in a large vacuum chamber on Earth, but quantification of thrust was not part of the experiment. 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 and reported significantly more modest gains.

Magnetoplasma sail (MPS)

In 2003 Funaki and others proposed an approach similar to the M2P2 design=26km and assumed a conversion efficiency that transferred a fraction of the solar wind momentum to the spacecraft. 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.

=100 m of 50 and 450km producing significant thrust with mass substantially less than the Magsail and hence significant acceleration. This paper detailed the MHD applicability test of equation that the characteristic length must be greater than the ion gyroradius to effectively transfer solar wind momentum to the spacecraft. In 2005 Yamakawa and others further described a potential trial.

as follows kg/m3 T is the local magnetic field flux density. Simulations have shown that the kinetic beta is smallest near the field source, at magnetopause and the bow shock.

differs from the thermal plasma beta the Boltzmann constant vacuum permeability specifies the relative energy of the injected plasma.

In 2005 Funaki and others published numerical analysis=0.1. In 2009 Kajimura published simulation results=1.8.

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. However experiments and numerical analysis determined that the solar wind cannot compress the magnetosphere and momentum transfer to the spacecraft is limited since momentum is transferred to injected plasma flowing out of the magnetosphere, similar to another criticism of M2P2. to achieve a plasma in equilibrium with the inflated magnetic field and therefore induce an equatorial diamagnetic current in the same direction as the coil current as shown in the figure, thereby increasing the magnetic moment of the MPS field source and consequently increasing thrust. In 2013 Funaki and others from equation or from equation .

In 2014 Arita, Nishida and Funaki published simulation results. They also reported that MPS increased the height of the magnetosphere by a factor of 2.6, which is important since it increases the effective sail blocking area.

where MHD is not applicable., which differs from the definition of a term by the same name in other studies. is 7.5 in the radial orientation. ) with the source indicated in the legend as follows for simulation results Arita14, Ashida14, Funaki13, and Kajimura10. 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. A thrust gain between 2 and 10 is common with the larger gains with a magnetic nozzle injecting plasma in one direction in opposition to the solar wind. The MHD applicability test of equation 72km. Therefore, the estimated force of the MPS is that of equation from equation

=810−21 kg/m3=500=72=410−8=105 11% from equation =1.6106=1.610−4 T from equation =5 the magnetic force only is 175 N from equation =105700 N.

that can be viewed as a propellant it has a specific impulse is the acceleration of Earth's gravity. Funaki and Arita=0.31 is 278km/s per newton of thrust force.

In 2015 Kajimura and others published simulation results for thrust performance with plasma injected by a magnetic nozzle, a technology used in VASIMR of 24 when the ion gyroradius (see equation , at the boundary of the MHD applicability test with some decrease for higher values of thermal beta.

In 2015 Hagiwara and Kajimura published experimental thrust performance test results with plasma injection using a magnetoplasmadynamic thruster (aka MPD thruster or MPD Arcjet) in a single direction opposite the solar wind direction and a coil with the axial orientation. = 60 = 60km.as compared with only plasma injection.

=810−21 kg/m3=500=72=410−8=60 28% from equation =1.6106=3.510−4 T from equation =5 the magnetic force only is 51 N from equation 611 N.

In 2017 Ueno published a design proposing use of multiple coils to generate a more complex magnetic field to increase thrust production. In 2020 Murayama and others published additional experimental results for a multi-pole MPD thruster. In 2017 Djojodihardjo published a conceptual design using MPS for a small (~500kg) Earth observation satellite.

In 2020 Peng and others published MHD simulation results for a magnetic dipole with plasma injection operating in Low Earth orbit at 500km 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.

Plasma magnet (PM)

The plasma magnet (PM) sail design introduced a different approach to generate a static magnetic dipole as illustrated in the figure. (m), each carrying a sinusoidal alternating current (AC) with the total current of (A) generated by an onboard power supply. The AC current applied to each coil is out of phase by 90° and consequently generates a rotating magnetic field (RMF) with rotational frequency (s−1) chosen that is fast enough that positive ions do not rotate but the less massive electrons rotate at this speed. The figure illustrates rotation using color coded contours of constant magnetic strength, not magnetic field lines. In order to inflate the magnetospheric bubble the thermal plasma beta must be high and initially a plasma injection may be necessary, analogous to inflating a balloon when small and internal tension is high. After initial inflation, protons and rotating electrons are captured from the plasma wind through the leaky magnetopause and as shown in the left create a current disc shown as transparent red in the figure with darker shading indicating greatest density near the coil pair and extending out to the magnetopause radius Rmp, which is orders of magnitude larger than the coil radius Rc (figure not drawn to scale). See RMDCartoon.avi for an animation of this effect. orders of magnitude larger than the input alternating current at the magnetopause boundary according to the MHD model of an artificial magnetosphere.

The magnetic field falloff rate was assumed in 2001 and 2006 =1. However, as described by Khazanov in 2003 and restated by Slough, Kirtley and Pancotti in 2011 and Kirtley and Slough in a 2012 NIAC report=2 as demanded by conservation of magnetic flux. Several MPS is a critical parameter in the determination of performance.

The RMF-induced rotating disc of electrons has current density (A m−2) at distance r, which states that flux conservation requires this falloff rate, consistent with a criticism of M2P2 by Cattell as follows: . A critical condition for the plasma magnet design rad/s as follows so that electrons in the plasma wind are magnetized and rotate but the ions are not magnetized and do not rotate: is the ion gyrofrequency (s−1) is the elementary charge be small enough such that collisions are extremely unlikely.

is derived by integrating the product of the square of the current density from equation with the result as follows: is the Spitzer resistivity (W m) of the plasma of ~1.210−3 where is the electron temperature assumed to be 15 eV,.

Starting with the definition of plasma wind force from equation rearranging and recognizing that equation , which can be substituted and then using equation yields the following expression must also satisfy equation , to which the comments following regarding a "tremendous leverage of power" do not address.

Note that a number of the examples cited in that do not meet the MHD applicability test of equation . From the definition of power in physics a constant force is power divided by velocity, the force generated by the plasma magnet (PM) sail is as follows from equation Comparing the above with Equation . Note from Equation .

Equation = 2,700kg/m3. Estimates of the coil mass.

The coil resistance is the product of coil material resistivity (Ω m) (e.g., ~310−8 is the radius of the coil wire as follows: . The peak current carried by a coil is specified by the RMF power and coil resistance from the definition of electrical power in physics as follows: from equation with result:=1.

Laboratory experiments validated that the RMF creates a magnetospheric bubble, electron temperature near the coils increases indicating presence of the rotating disc of electrons and that thrust was generated. Since the scale of a terrestrial experiment is limited, simulations or a flight trial was recommended. Some of these concepts adapted to an ionospheric plasma environment were carried on in the plasma magnetoshell design.

In 2022 Freeze, Greason and others published a detailed design for a plasma magnet. A transit time to Jupiter of 25 days was reported for a 21kg spacecraft design launched in a 16 U Cubesat format.

=2 in 2011 and 2012,=810−21 kg/m3=500=72=410−8=105=410−4 T from equation . The required RMF power from equation is 13=10 A from equation =2 kA from equation =5 the plasma magnet force from equation is 197 N. The magnetic force only for the above parameters is 2.8 N from equation and therefore the plasma magnet thrust gain is 71. The performance comparison=2 results in a transit time of ~100 days.

Plasma magnetoshell (PMS)

A 2011 paper by Slough and others and a 2012 NIAC report by Kirtley investigated use of the plasma magnet technology with 1/r2 magnetic field falloff rate for use in the ionosphere of a planet as a braking mechanism in an approach dubbed Plasma magnetoshell (PMS). The magnetoshell creates drag by ionizing neutral atoms in a planet's ionosphere then magnetically deflecting them. A tether attaching the plasma magnet coils to the spacecraft transfers momentum such that orbital insertion occurs. Analytical models, laboratory demonstrations and mission profiles to Neptune and Mars were described.

In 2017, Kelly described using a single-coil magnet with 1/r3 magnetic field falloff rate and more experimental results. In 2019 Kelly and Little published simulation results for magnetoshell performance scaling.=1,000kg and total magnetoshell system mass of 1,623kg, 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=6km is required for a 5,000kg spacecraft and must average 50kN 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= 500= 5106 m−3 = 1.6710−27 kg a proton mass = 8.410−21 kg/m3=5 where applicable. Equation ≈ 36 nT, equation ≈ 72=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, equation defines the force for the plasma magnet (PM) is from equation for the magneto plasma sail (MPS) is the simulation and/or experimentally determined value with force defined equation to account for thrust loss due to operation in a kinematic region. The last column headed MPS+MPD adds a magnetoplasma dynamic thruster are design parameters. Equation .

=2106 A/m to account for warmer temperatures in the solar system. The plasma magnet uses AC power for the rotating magnetic field, PRMF as specified in Equation = 2,700kg/m3=5 =6,500kg/m3=51.6 106 were chosen to match the thrust gain from simulation and scaled experimental results and meet the superconducting-coil critical current constraint.

Equation =5mm. Equation . Equation kA as defined in equation .

Superconducting coils do not require continuous power (except possibly for cooling); however, the plasma magnet design does, as specified in equation . An estimate for the plasma magnet power supply mass assumes ~3kg/W for nuclear power in space ≈ 7.8108 . For comparison purposes the time for a Hohmann transfer from Earth orbit to Jupiter orbit is 2.7 years (almost 1,000 days) but that would allow orbital insertion whereas a magnetic sail would do a flyby unless the magnetosphere and gravity of Jupiter could provide deceleration. Another comparison is the New Horizons interplanetary space probe with a 30kg payload that flew by Jupiter after 405 days on its way to Pluto. performance occurs for the PM and MPS designs due primarily to much reduced coil and other mass. As described in the M2P2 section=1 was questionable and hence it was not included in this table. Simulations and experiments as described in the MPS section=2 is valid with injection of plasma to inflate the magnetic field in a manner similar to M2P2. As described in the PM section=2,=1 being very optimistic. The classic Magsail (MS) design generates the most thrust force and has considerable mass but still has relatively good time performance. Parameters for the other designs were chosen to yield comparable time performance subject to the constraints previously described. As described above and further detailed in the section for the respective design, this article contains the equations and parameters to compute performance estimates for different parameter choices.

Criticisms

In 1994 Vulpetti published a critical review regarding viability of space propulsion based on solar wind momentum flux. 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 and noted in equation (B1) that the Bolonkin paper equation (2) assumed that the plasma had a large net negative electrical charge. The plasma charge varies statistically over short intervals and the maximum value has negligible impact on Magsail performance. Furthermore, he argued that observations by many spacecraft have observed compression of a magnetic field by dynamic (or ram) pressure that did not depend on particle charges.

In 2017, Gros published results that differed from prior magsail work. A major result was the Magsail kinetic model of equation of prior work.

Fictional uses in popular culture

Magnetic sails have become a popular trope in many works of science fiction although the solar sail is more popular:

1. The ancestor of the magsail, the Bussard magnetic scoop, first appeared in science-fiction in Poul Anderson's 1967 short story To Outlive Eternity, which was followed by the novel Tau Zero in 1970.

2. The magsail appears as a crucial plot device in The Children's Hour, a Man-Kzin Wars novel by Jerry Pournelle and S.M. Stirling (1991).

3. It also features prominently in the science-fiction novels of Michael Flynn, particularly in The Wreck of the River of Stars (2003); this book is the tale of the last flight of a magnetic sail ship when fusion rockets based on the Farnsworth-Hirsch Fusor have become the preferred technology.

4. GURPS Spaceships features both solar sails and magnetic sails as possible methods of spacecraft propulsion.

Although not referred to as a "magnetic sail", the concept was used in the novel Encounter with Tiber by Buzz Aldrin and John Barnes as a braking mechanism to decelerate starships from relativistic speed.

See also

• interacts with magnetosphere in similar manner to magsail

• (Magnetized beamed plasma propulsion)a beam-powered variant of mini-magnetospheric plasma propulsion (M2P2).

• Other methods of spacecraft propulsion used to change the velocity of spacecraft and artificial satellites.

References