[Daumic (OP)]

A series of articles published recently (1) (2) described an effective shielding against a magnetic field. This effect is obtained by associating two concentric shells, one made of a superconductor, the other made of a ferromagnetic material. The shielding makes it possible to mask a volume from an external magnetic field or to dissimulate a magnetic field from the external world. It can in particular move away a magnetic pole from its opposite and thus to simulate a magnetic monopole artificially.

Perhaps this magnetic shielding would make it possible to create an electromagnetic sail that means a system of propulsion which would use the natural magnetic fields, in particular the terrestrial magnetic field. Imagine a ring of electric current placed in this magnetic field. Laplace forces that are exerted on the electric current cancel: no translation of the ring is possible. On the other hand, if part of this ring is taken in magnetic shielding described above, the action of the magnetic field on the electrical current in the masked section is cancelled. Laplace forces that are exerted on the whole of the electric current do not cancel any more: the ring can be put moving.

Is this sort of electromagnetic veil possible? 

(1) Gomory, F. et al. Experimental realization of a magnetic cloak. Science 335, 1466 (2012)

(2) Prat-Camps, J. et al. A Magnetic Wormhole. Sci. Rep. 5, 12488; doi: 10.1038/
srep12488 (2015)

[chris]

An interesting suggestion, but I don't know the answer; it needs a physics brain like Evan or Alan on this!

[ijaz]

https://en.wikipedia.org/wiki/Magnetic_sail

[Daumic (OP)]

wikipedia.org/wiki/Magnetic_sail

I know this sort of magnetic sail. It uses the effect of a magnetic field generated by a superconducting coil on solar wind. This project promises an improvement of interplanetary flights but cannot be used for launching from Earth. I hope that electromagnetic sail with magnetic shielding can serve for launching from Earth.

[wolfekeeper]

Magnets have a range that is a few times their size. So if you want a magnet to work at a range of 100km, it has to be roughly 20+km in diameter. That would be a BIG vehicle!

The fact that the Earth is really big doesn't help. If it did, magnets would fly all by themselves. The reason it doesn't, if you like, is that the repulsion to one pole of the magnet, from the big magnet that is the Earth, is balanced by the attraction of the other pole. Only if the magnets are similar size can the poles be far enough apart to give you lift and repulsion.

To get maximum traction they have to be roughly the same size.

Magnetic shielding is really just using magnets to cancel out other magnets. Even superconducting levitation works like that.

[Daumic (OP)]

This electromagnetic sail does not use the repulsion or the attraction of magnetic poles but the Laplace forces applied on an electric current by a magnetic field.

[wolfekeeper]

Irrelevant, you said:

"Perhaps this magnetic shielding would make it possible to create an electromagnetic sail that means a system of propulsion which would use the natural magnetic fields, in particular the terrestrial magnetic field."

The terrestrial magnetic field is produced by the Earth, which is an enormous magnet. Not even superconducting magnets; magnets which can exclude all magnetism from within them fly away from the Earth.

[evan_au]

Laplace Force

The Laplace Force is a subset of the more general Lorentz Force.

Laplace forces that are exerted on the whole of the electric current

A small scale test has been conducted with a wire passing through Earth's magnetic field, as a way to lower the orbit of obsolete satellites. In principle, you could also boost a satellite orbit, using power from a solar cell.

if part of this ring is taken in magnetic shielding described above, the action of the magnetic field on the electrical current in the masked section is cancelled. Laplace forces that are exerted on the whole of the electric current do not cancel any more: the ring can be put moving.

A superconducting magnetic shield excludes an external magnetic field by setting up an internal supercurrent to oppose the external magnetic field (the Meissner effect).

So I don't see how this partial magnetic shield by itself could translate into linear motion inside Earth's weak magnetic field (or the Sun's even weaker magnetic field, at Earth's distance).

You can't get something for nothing. The kinetic energy to accelerate the satellite must come from somewhere - presumably the from the current in the coil.

Earth's magnetic field is used to orient small satellites using a magnetic torquer.

[Daumic (OP)]

So I don't see how this partial magnetic shield by itself could translate into linear motion inside Earth's weak magnetic field (or the Sun's even weaker magnetic field, at Earth's distance).

It is not the magnetic shield that translates inside the terrestrial magnetic field but the ring of electric current.

You can't get something for nothing. The kinetic energy to accelerate the satellite must come from somewhere - presumably the from the current in the coil.

Yes, the electromagnetic sail need electric energy when it moves inside the terrestrial magnetic field. The movement of the electric conductor inside the magnetic field generates a counter-voltage that stop the electric current. So the sail need electric energy to sustain the electric current.

[Daumic (OP)]

The electromagnetic sail as space launcher

If this electromagnetic sail is possible, I see it as a space launcher. The terrestrial magnetic field extends to several thousands kilometers from ground. It could thus provide a support to an electromagnetic sail until in orbit. 

To obtain an effective sail, the material constituting the conducting ring must carry the electric current most intense possible. The best choice for this material is a superconductor. To ensure that this superconductor can be used for an electromagnetic sail, the minimal condition is Laplace force that is applied to it higher than its weight. Following simple calculation shows that two criteria are significant to satisfy this condition: the critical current density that can carry the superconductor and its density. 

Criteria of the superconductor for an electromagnetic sail

Let a conducting square circuit located at the terrestrial equator. The circuit is orthogonal to the terrestrial magnetic field. The direction of the electric current is such as Laplace forces are directed towards the outside of the circuit. The forces applied to the western and eastern parts of the circuit cancel each other. The low part of the circuit is coated with the magnetic shielding described in my first message and thus does not undergo Laplace force. The high part of the circuit undergoes a Laplace force that is not compensated. What should be this Laplace force to support the weight of the whole circuit?

F = I. B. L

With  F: Laplace force applied to the higher part of the circuit,
        I: intensity of the electric current,
        B: horizontal component of the terrestrial magnetic field,
        L: length of the higher part of the circuit.


P = 4. d. v. g

With  P: weight of the whole circuit,
        d: density of the circuit material,
        v: volume of the higher part of the circuit,
        g: acceleration of terrestrial gravity.

It is necessary that:    F > P 

I. B. L > 4. d. v. g

With  s: section of the circuit,
        j: density of the electric current.

j. s. B. L > 4. d. g. s. L

j. B > 4. d. g

Finally, to obtain a Laplace force higher than the weight, it is necessary that:

j > 4. d. g/B

The current density that the superconductor must carry to be used in an electromagnetic sail depends on its density and the ratio g/B.

First criterion: density of the superconductor

Among all known superconductors, it seems to me that the magnesium diboride shows the most interesting characteristics: a low density of 2.57 g/cm3 and a critical current density of  10000 A/mm2 (3). MgB2 seems to satisfy the minimal condition to constitute an electromagnetic sail. For example, in a horizontal magnetic field of 40 µT, the density of current necessary to ensure that the Laplace force equalizes the weight of a square circuit of MgB2 is 2520 A/mm2, level much lower than the critical current density of material.

To obtain a complete electromagnetic sail, it remains to add the mass of the magnetic shielding and especially the mass of the cooling system because the magnesium diboride becomes superconductive only below 40 K. 

Second criterion: the ratio g/B

The Internet site (4) calculates the parameters of the terrestrial magnetic field anywhere on the terrestrial sphere and in altitude. It shows that the horizontal component of the terrestrial magnetic field, the only usable for a space launching, is maximum at the equator.

The acceleration of terrestrial gravity g also varies according to altitude. The following mathematical formula (5) calculates g:

g(h) = g0/(1 + (2h/R) + (h2/R2))

With  g0: acceleration of terrestrial gravity to altitude 0,
        g(h): acceleration of terrestrial gravity to altitude h,
        h: altitude,
        R: terrestrial radius.

The following table shows the variation of the magnetic field and terrestrial gravity according to altitude:

 [ Invalid Attachment ]

The data of this table are shown in the following graph:

 [ Invalid Attachment ]

These data show that the magnetic field decreases more quickly than the acceleration of terrestrial gravity when altitude increases. The g/B ratio thus increases with altitude. This ratio determines the effectiveness of the electromagnetic sail. The propulsion force of the electromagnetic sail decreases with altitude. As the electric current in the superconductor cannot exceed the critical current, there is a limit altitude beyond that the sail ceases working.


(3)  [http://iopscience.iop.org/article/10.1209/epl/i2002-00479-1/meta;jsessionid=E3DÇ22DC2891E013CCDD261AE163683.c1]

(4)  [http://www.geomag.bgs.ac.uk/data_service/models_compass/igrf_form.shtml]

(5)  [http://e.m.c.2.free.fr/poids-and-gravitation.htm]

[Atomic-S]

It seems to me that the thing that undoes any attempt to shield part of a circuit so that it becomes magnetically inactive, thereby allowing the other part to exert an unbalanced force, or to be exerted upon by an unbalanced magnetic force, is the very currents that are induced in the superconducting shield by the shielding process. Consider a superconducting tube through which part of a circuit passes axially.  When current is turned on in the circuit, in order to block the magnetic field from penetrating the superconducting tube, there must be generated in the superconducting tube a countercurrent running in the opposite direction. This countercurrent runs along the inside surface, creating effetively a coaxial cable. So, far, so good. But the countercurrent runs into the end of the tube, where it must now go someplace. To maintain B = 0 inside the material of the tube, it must turn around and head back across the outside surface of the tube.  So that, although the current in the central wire has been made magnetically invisible by the shielding effect, we now have a new equal current running along the outside surface of the tube. This will cause the exposed part of the wire to move one way, and the tube to move the opposite way.  The amount of distance that the wire will get using this form of propulsion is limited by the radius of the tube.  Not suitable for space flight.

[Daumic (OP)]

It seems to me that the thing that undoes any attempt to shield part of a circuit so that it becomes magnetically inactive, thereby allowing the other part to exert an unbalanced force, or to be exerted upon by an unbalanced magnetic force, is the very currents that are induced in the superconducting shield by the shielding process. Consider a superconducting tube through which part of a circuit passes axially.  When current is turned on in the circuit, in order to block the magnetic field from penetrating the superconducting tube, there must be generated in the superconducting tube a countercurrent running in the opposite direction. This countercurrent runs along the inside surface, creating effetively a coaxial cable. So, far, so good. But the countercurrent runs into the end of the tube, where it must now go someplace. To maintain B = 0 inside the material of the tube, it must turn around and head back across the outside surface of the tube.  So that, although the current in the central wire has been made magnetically invisible by the shielding effect, we now have a new equal current running along the outside surface of the tube. This will cause the exposed part of the wire to move one way, and the tube to move the opposite way.  The amount of distance that the wire will get using this form of propulsion is limited by the radius of the tube.  Not suitable for space flight.

Yes, when the electric current flows in the ring circuit, its magnetic field induces electric currents in the superconductive shield. But the direction of this current in one side of the outside surface of shield is the opposite in the other side of the outside surface of shield. So the effect of the terrestrial magnetic field on this current is not an opposed force of the force applied on the naked wire but a torque applied on the shield.

Furthermore, the superconducting shielding acts also against the terrestrial magnetic field. The natural magnetic field induces electric currents in the superconductive material that generate a counter magnetic field. So the magnetic field is null at the outside surface of shield.

[evan_au]

Second criterion: the ratio g/B

The graph suggests that B is comparable to g (to within an order of magnitude).

But the scale shows g in m/s², while B is in μT.
To provide comparable units, B should be measured in Tesla.
This suggests that the Earth's magnetic field might be about 6 orders of magnitude too weak to do what you want?

Also, be careful with the mass of insulation, refrigeration and power distribution for a megaproject like this. Mechanical rigidity is also a problem with something that is long and thin.

[Daumic (OP)]

The graph suggests that B is comparable to g (to within an order of magnitude).

But the scale shows g in m/s2, while B is in μT.
To provide comparable units, B should be measured in Tesla.
This suggests that the Earth's magnetic field might be about 6 orders of magnitude too weak to do what you want?

Also, be careful with the mass of insulation, refrigeration and power distribution for a megaproject like this. Mechanical rigidity is also a problem with something that is long and thin.

The Tesla, unit of magnetic induction, has a very great value. So the fact that the terrestrial magnetic field is expressed with micro Tesla unit doesn’t mean that it is weak. The interest of the graph is to show the variation of the ratio g/B with the altitude. Compare g and B has no sense.

Yes, the mass of insulation, cooling system and magnetic shielding is a problem. This is the reason that I have noticed in my message “To obtain a complete electromagnetic sail, it remains to add the mass of the magnetic shielding and especially the mass of the cooling system because the magnesium diboride becomes superconductive only below 40 K.”

[Daumic (OP)]

An energy source is necessary

The electric current in a superconductor circulates without loss of energy. Can one imagine that an electromagnetic sail can go in space without energy source other than that necessary to the starting of the electric current? In fact, not, an energy source is necessary for the electromagnetic sail because its displacement in the terrestrial magnetic field generates an electric counter voltage in the superconductor that cancels the electric current. An energy source is necessary to maintain the electric current in the electromagnetic sail during space launching.

The Laplace force in the electromagnetic sail is:

F = I. B. L

With  F: Laplace force applied to the higher part of the circuit,
        I: intensity of the electric current,
        B: horizontal component of the terrestrial magnetic field,
        L: length of the higher part of the circuit.

If the circuit moves at the speed v, it will appear a counter voltage:

V = B. L. v 

With  V: counter voltage applied to the higher part of the circuit,
        v: speed of the circuit in the magnetic field.

The power p needed to maintain the electric current is:

p  = I. V 

This electric power can be still expressed by:

p  = (F / B. L ). ( B. L. v )  = F. v

The needed electric power is exactly the upward mechanical power.

[Atomic-S]

Yes, when the electric current flows in the ring circuit, its magnetic field induces electric currents in the superconductive shield. But the direction of this current in one side of the outside surface of shield is the opposite in the other side of the outside surface of shield. So the effect of the terrestrial magnetic field on this current is not an opposed force of the force applied on the naked wire but a torque applied on the shield.

The currents in the superconductive shield do not circulate around the wire in the middle, but travel parallel or antiparallel to it. That is because the wire creates a magnetic field at right angles to the wire, but that field, on expanding into the superconductor, induces currents at right angles to the field, which is to say, again parallel or antiparallel to the original current. Antiparallel on the inside surface and parallel on the outside surface.

[Daumic (OP)]

A space launching by electromagnetic sail

The orbiting of an object requires 32 MJ of energy for each launched kg. This energy necessary to the propulsion must be provided to the vehicle equipped with the electromagnetic sail. If the electromagnetic sail does not allow energy saving during launching, that can it offer moreover than one traditional space launcher with rocket?

The expression of the mechanical power (p = F. v) suggests a solution: the electromagnetic sail could be used as slow space launcher. If we limit the climbing speed, about a few tens of m/s, the power required to maintain electric current in sail becomes very moderate. 

The power would be sufficiently moderate to be provided by photovoltaic panels or a fuel cell. The most effective solar panels currently provide 500 W/kg. Two tons of these panels can provide energy to propel a vehicle of a total weight of 10 tons at 10 m/s. But these two sources of electric energy have each one a problem: alternation between day and night will obstruct the electric production of the photovoltaic panels, the fuel cell must be supplied by hydrogen and oxygen onboard the vehicle that is then subjected to the problem of mass ratio of the current rockets.

The electromagnetic sail seems to me adapted to a new system of propulsion studied for a few years: propulsion by beams. This mode of propulsion consists providing the space vehicle energy by an electromagnetic beam, laser or microwave. To take again the previous example, a microwave beam of 1 MW could feed the electric power required by a vehicle of 10 tons at climbing speed of 10 m/s.

A launching with microwave beam would occur in the following way:

- the launching vehicle is equipped with an electromagnetic sail, a microwave antenna, a small rocket engine of orbital operation and payload,

- a microwave antenna on the ground supplies energy to the vehicle,

- the trajectory of the vehicle is vertical; the initial slow speed of the vehicle is maintained all along the flight, by this way the power required (p = F. v)  to maintain the current in the superconductive ring remains moderate,

- with altitude, the terrestrial magnetic field decreases more quickly than gravitational attraction; to maintain the same force (F = I. B. L) the electric current in the superconductive ring of the sail must increase to compensate the reduction of the geomagnetic field but does not have to reach the critical intensity,

- the electromagnetic sail is stopped when an altitude of about 7000 km is reached; the potential energy of the vehicle at this altitude is equivalent to the kinetic energy of an orbiting at low altitude, so the complete orbiting of the payload requires nothing any more but one small orbital engine,

- the electromagnetic launcher composed of the sail and the antenna separates from the payload and its rocket engine,

- the electromagnetic launcher returns on Earth at low speed according to the same vertical trajectory; this descent is done without the assistance of the microwave beam because the downward movement in the geomagnetic field generates an electric tension in the superconductive ring; the dissipation of this electric power in a resistive circuit makes it possible to convert the kinetic energy of the vehicle into heat easy to evacuate by a radiator; this descent can be done at low speed thanks to this electromagnetic braking, 

- the rocket motor of orbital operation is ignited to adjust the orbit of the payload.

The electromagnetic sail associated with a microwave beam would replace the first stages of a traditional rocket.

[alysdexia]

The electromagnetic sail associated with a microwave beam would replace the first stages of a traditional rocket.

What is the propellant?

[Daumic (OP)]

What is the propellant?

There is no propellant. I hope obtain a propulsion with the association of a superconductive ring and a magnetic shield. For more information, you can read the first message of the topic.

[alysdexia]

What is the propellant?

There is no propellant. I hope obtain a propulsion with the association of a superconductive ring and a magnetic shield. For more information, you can read the first message of the topic.

I already did.  In that message the propellant was the earth.