Editing Magnetic sail (section)

== Overview ==
[[File:Magnetic rope.svg|thumb|upright]]
The [[#Modes of operation|Modes of operation]] section describes the important parameters of [[#Plasma mass density and velocity terminology and units|plasma particle density and wind velocity]] in conjunction with a use case for:

* Operation in a [[#Acceleration/deceleration in a stellar plasma wind|stellar (e.g., Sun) wind]].
* [[#Deceleration in interstellar medium (ISM)|Deceleration in the '''interstellar medium''' (ISM)]].
* Operation in a [[#In a planetary ionosphere|planetary ionosphere]] or [[#In a planetary magnetosphere|planetary magnetosphere]].

The [[#Physical principles|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.
[[File:VFPt ringcurrent.svg|thumb]]
[[Charged particle]]s 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|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 interstellar medium (ISM)|deceleration in the interstellar medium (ISM)]] mode of operation the velocity is a significant fraction of light speed, for example 5% c,<ref name=":14" /> the gyroradius is ~ 500&nbsp;km for protons and ~280 m for electrons. When the magsail magnetopause radius is much less than the proton gyroradius the [[#Magsail kinematic model (MKM)|magsail kinematic model]] by Gros in 2017,<ref name="gros2017" /> 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 [[Magnetic moment#Amperian loop model|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#Visualization|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 [[#MHD model|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 [[#MHD applicability test|applicability of magnetohydrodynamic (MHD)]] theory, which models charged particles as fluid flows, is that to achieve maximum force the radius of the [[#Artificial magnetospheric model|artificial magnetosphere]] be on the same order as the ion gyroradius for the plasma environment for a [[#Modes of operation|particular mode of operation]]. Another important condition is how the proposed design affects the magnetic field falloff rate inside the magnetosphere, which impacts the field source mass and power requirements. For a radial distance r from the spacecraft's magnetic field source in a vacuum the magnetic field falls off as <math>1/r^{f_o}</math>, where <math>f_o</math> is the falloff rate. Classic [[magnetic dipole]] theory covers the case of <math>f_o</math>=3 as used in the magsail design. When plasma is injected and/or captured near the field source, the magnetic field falls off at a rate of <math>1 \leq f_o \leq  2</math>, a topic that has been a subject of much research, criticism and differs between designs and has changed over time for the plasma magnet.  The M2P2 and plasma magnet designs initially assumed <math>f_o</math>=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|magnetic field model]] where <math>1 \leq f_o \leq  3</math> and asserted that an <math>f_o</math>=2 falloff rate was the best achievable. In 2011 the [[#Plasma magnet (PM)|plasma magnet]] author<ref name=":22" /> changed the falloff rate <math>f_o</math> from 1 to 2 and that is the value used for the plasma magnet for performance comparison in this article. The [[#Magnetoplasma sail (MPS)|magnetoplasma sail (MPS)]] design is an evolution of the M2P2 concept that has been extensively documented, numerically analyzed and simulated and reported a falloff rate <math>f_o</math> between 1.5 and 2.
[[File:MFM relative force vs AU.png|thumb|upright=1.5]]
The falloff rate <math>f_o</math> has a significant impact on performance or the mode of operation [[#Acceleration/deceleration in a stellar plasma wind|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]] the impact of falloff rate <math>f_o</math> on relative force F from Equation {{EquationNote|MFM.6}} versus distance from the Sun ranging from 1 to 20 AU, the approximate distance of Neptune. The distance to Jupiter is approximately 5 AU.  Constant force independent of distance from the Sun for <math>f_o</math>=1 is stated in several plasma magnet references, for example Slough<ref name="Slough2006" /> and Freeze<ref name=":11" /> and results from the effective increase in sail blocking area to exactly offset reduced plasma mass density as a magnetic sail spacecraft accelerates in response to the plasma wind force away from the Sun. As seen from the illustration the impact of falloff rate <math>f_o</math> 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|General kinematic model]] section where researchers report results from a compute intensive method that simulates individual particle interactions with the magnetic field source.<ref name=":25" />