User:Dmcdysan/sandbox/magnetic sail

A magnetic sail is a proposed method of spacecraft propulsion that uses a static magnetic field to deflect a plasma wind of charged particles radiated by the Sun or a Star as shown at the left of the figure, thereby accelerating a spacecraft shown as a red dot in the center of the illustration attached to a red loop that generates a magnetic field that under certain conditions, summarized in the overview section, creates an artificial magnetosphere shown by the small black circle surrounding the spacecraft and field source at. A magnetopause surrounds the magnetosphere shown by the blue and yellow lines on the right of the illustration with a bow shock shown in yellow forming between the magnetopause and the Sun as shown in the center of the figure. The term magnetospheric object refers to the magnetosphere, magnetopause and the bow shock. Charged particles in the plasma are deflected by the bow shock and magnetopause that together create an effective sail blocking area that exerts a thrust force that acts on the magnetic field, which in turn exerts a force on the magnetic field source attached to spacecraft in the same direction as the plasma wind.

EDITING STOPPED 9/18/222 at: MHD Applicability

MHD Model

CUT: For a large current loop following the Biot–Savart law ${\textstyle C_{d}}$ is a different value than that of a dipole but also a function of tilt angle.

Plasma magnetoshell (PMS)

CUTS: NIAC funded studies in 2014 and 2016 and in 2018 Kelly further detailed this approach with details for Mars and Neptune. THESIS

Since the target plasma environment is a planetary atmosphere with characteristics different from that of the solar wind or the ISM, a different design is required.

To reduce complexity the model assumed a single ion species of H₂ (Jupiter, Saturn, Uranus, Neptune) or Argon (Ar) since it has an atomic mass unit (amu) similar to N₂ (Titan, Earth) and CO₂ (Mars, Venus).

1623=(1000+26+56)*1.5, where 1.5 is "mass gain"

CUT Citations

M2P2 Lab Test

Djohardaro

Funaki 2009

Cruz

Funaki 05

Zubrin 1990

Gros Critique

Summarized, critical comments removed.

In 2017 Gros reported on numerical examples for the Magsail kinematic model. For a high speed mission to Alpha Centauri, with initial velocity before deceleration of  $v_{0}=c/10$ with section 4.2 reporting a coil mass of 1500 tons and Equation (23) a coil radius of $R$=1600 km. There is an internal inconsistency in the coil radius calculation. Using the parameters from the paper Equation (22) for the coil radius $R$ yields a value over 10 times less than the value reported in Equation (23). Section 4.1 gave an estimated stopping distance $x_{max}$of 0.37 (ly) and a total travel time of 58 years.

Perakis & Hein 2016 Preprint

Deleted from magnetic sail on 9/7/22, reason given preprint is not WP:RS.

In 2016 Perakis and Hein preprint described and analyzed a combination of magnetic sail and electric sail for interstellar deceleration that was further analyzed by Sharma and others in 2020.v A conservative assumption that would make the results pessimistic was an ISM plasma density was 0.03 (cm^-3), significantly less than other estimates for the G-cloud for approach to Alpha Centauri of 0.1 (cm^-3). One observation was that the magnetic sail was best for deceleration from higher velocities while the electric sail better at lower velocities. An example for deceleration from 5% of light speed to interplanetary velocities (10-100 km/s) with both sails as 29 years, electric sail alone as 35 years and magnetic sail alone of 40 years for a spacecraft with coil radius of =1,000 km of mass 8.25 tonnes. The estimate of 15% additional mass for tethers and support structures is significantly less than Equation MS.6.

Another issue is potential error. Wrote Perakis and Hein on ResearchGate August 2022, heard no response.

These results may be optimistic since Equation (3) (which cites Equation (1)) have a significant difference for the magsail force equation as compared with the Magnetic field model force of Equation MFM.5 as stated by multiple citations as detailed in the text following that equation. Citing a 2012 Freeland paper that was not available online the exponent of the term on the right side of the force equation was 3/2. In a 2015 Freeland paper of the same title, Equation (108) stated an exponent value of 2/3 as corroborated by other citations following Equation MFM.5. Potentially impacted are statements that the magnetic sail is more effective at higher velocities since a smaller exponent means that magnetic force is proportional to  versus  as assumed in these papers. This difference means that magnetic sail component of these calculations could be optimistic and the optimization point between use of magnetic and electric sails could change.

2021 Zhenyu Yang

Duplicate text with "History of Concept" Deleted 9/7/22. Shortened summary paragraph.

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. The concept involves a superconducting ring like magsail to generate a magnetic field but adds an electron gun at the center of the coil to generate an electric field as done in an electric sail that deflects positive ions in the plasma wind thereby providing additional thrust. With the additional thrust of the electron gun powered electric sail, the size of the superconducting ring can be markedly reduced decreasing the overall system mass significantly.

Crowl 2017 Critique

REVISED For launch from 0.5 AU Table 2 reported a coil radius  of 66 km at a mass of 545 kg using Equation MS.5 multiplied by a factor of 5 to account for additional mass needed for structure. Table 3 reported the total travel time to 1,000 AU to reach the vicinity of Planet nine for a 500 kg payload as 29 years.

CUT The mass values of Table 2 and Table 3 are optimistic by a factor of approximately 10 when compared with Equation MS.5.

Slough Critique

CUT from History: Funding for NIAC in 2007 was cancelled and a Phase III project was never funded.

CUT: $f_{o}$ dropped by Slough in 2012

As noted by Slough when operating in the solar wind where density falls off inversely proportional to the square of the distance from the sun (see Equation MO.1) when $f_{o}$=1, then Equation MFM.5 predicts constant thrust force. When $f_{o}$>1 then Equation MFM.5 predicts thrust force decreasing with distance from the Sun.

For $R_{mp}$= 30 km, $B_{mp}$= 50 nT and power from the solar wind from Equation (14) is $P_{sw}$= 6.3 MW corresponding to a force of 15 N at $v_{sw}$ = 450 km/s,

CUT: which contradicts the text following Equation (10) citing $P_{sw}$=700 MW.

REVISED: Starting with the definition of plasma wind power from Equation MHD.4, rearranging and recognizing that Equation PM.3 can be substituted and then using Equation MFM.1 yields the following expression

$P_{w}={\frac {C_{d}\,\mu _{0}}{4\,\eta _{p}\,C_{SO}}}u\,P_{RMF}\,R_{0}{\biggl (}{\frac {R_{0}}{R_{mp}}}{\biggr )}^{2(f_{o}-1)}{\frac {f_{o}^{2}}{2f_{o}-1}}$ (PM.4)

which is the same as Equation (10) for $f_{o}=1$, with the text following that equation incorrectly giving an example where $P_{RMF}$ and $R_{0}$ are chosen independently resulting in a predicated gain of 70,000 of achieved thrust power $P_{w}$over input power ${\textstyle P_{RMF}}$, when in fact a system of polynomial equations requires two equations for two variables. In other words, specification of $P_{RMF}$ and $R_{0}$ must also satisfy Equation PM.3, which the cited example does not.

CUT: For $R_{mp}$= 30 km, $B_{mp}$= 50 nT and power from the solar wind from Equation (14) is $P_{sw}$= 6.3 MW corresponding to a force of 15 N at $v_{sw}$ = 450 km/s.

CUT: Thus the large mass of the magsail is avoided and the continuous injection of plasma in M2P2 or MPS is at least reduced in the steady state.

Deceleration in the ISM

CUT 9/11/22 because details are in corresponding sections, no citation for PM or MPS.

Only Freeland 2015 and the Zubrin/Gros comparison remain, so a comparison table is not necessary.

Ensure that all information from here is moved to these descriptions.

The table compares performance measures for the magnetic sail designs with the following parameters for deceleration in the ISM on approach to Alpha Centauri: initial velocity $u_{im}$= 1.5x10⁷ km/s (5% of light speed), number density $n_{i}$= 1x10⁵ (m⁻³), ion mass $m_{i}$ = 1.67x10⁻²⁷ kg a proton mass, resulting in mass density $\rho _{im}=m_{i}n_{i}$ = 1.67x10⁻²² (kg/m³), and coefficient of drag $C_{d}$ as described below. Equation MHD.2 gives the magnetic field magnetopause at the beginning of deceleration as $B_{mp}$≈ 15 μT, Equation MHD.5 gives the ion gyroradius $r_{g}$≈ 509 km for $C_{Li}$=2. The target magnetopause radius was chosen to be $R_{mp}$=500 km (except when a specific example stated otherwise) to meet the #MHD applicability test. Table entries in bold face are from a cited source as described in the following.

The usage of equations to determine performance measures are the same as for Acceleration/deceleration with the solar wind case with the following exceptions and explanations. The first Magsail (MS) column is from Freeland with items in boldface from that paper matching exactly the entries in the table.The second MS column is from the Magsail kinematic model section. At initial velocity of 5% light speed there is little difference between the MHD based modeland the kinematic model for the parameters stated in the table. The plasma magnet has been proposed for deceleration in the ISM and there is a column for magnetic field falloff rate $f_{o}$=1 and $f_{o}$=2 analogous to the solar wind case. No citations were found proposing use of M2P2 or MPS for the ISM deceleration case so these are not included in the table.

An optimistic approximation is constant acceleration $a$ (m/s²), for which the time to decelerate from a velocity $V$ of 5% of light speed is $T_{V}\approx V/a$ (days) and time to cover a specified distance of 0.5 light year (ly), $D$ ≈ 4.7x10¹² km, is ${\textstyle T_{D}\approx {\sqrt {2D/a}}}$ (days). Note from Equation MFM.5 for $f_{0}$=3 that force is proportional to $v^{4/3}$for velocity $v$ and therefore decreases with decreasing velocity and would increase deceleration time and distance. See the Magsail kinematic modeland magsail specific design mission profiles for more detailed examples.

General kinematic model - Ashida 2014

CUT since Ashida 2014 curve fit effective range does not cover some relevant examples.

The Ashida14 model computes thrust force for the Kinetic Model (KM)  $F_{KM}$ (N) from the magnetic moment $\mathbf {m}$ (A m²), particle density $n_{i}$ (m^-3) and plasma wind velocity $u$ (m/s) via a curve fit to simulation results from Equation (7) and Figure 9 is as follows:

$F_{KM}\approx 3.57\times 10^{-26}\,n_{i}^{1.15}\,u^{0.92}\,\mathbf {m} ^{1.03}{\frac {4\pi }{\mu _{0}}}$ (GKM.1)

where the $(4\pi )/\mu _{0}$ term is a units conversion factor from (A m²) to (Wb m) and 10⁶ < $(4\pi \,\mathbf {m} )/\mu _{0}$ < 10¹³ bounds the above to the region where MHD is not applicable and the curve fit for simulation results.