Minefields are areas containing concealed, explosive devices designed to cause damage and death to hostiles in the region. This suggestion explores the possibility of mining a 1000km x 1000km x 1000km volume of outer space with a uniform distribution of 1000 mines that use positronium as a payload.
The proposal has been designed with the following goals in mind:
- The minefield should cover as big a volume of space as possible and be scalable to larger volumes.
- The minefield should be as quick to establish as possible.
- The minefield should not be easily detectable using long-range scanners.
- The minefield should have a high chance of intercepting hostiles passing within it.
- The minefield should be capable of inflicting a high degree of damage upon hostiles that it intercepts.
- The minefield should remain operable for a long period of time and remain largely self-sufficient.
- The suggestion should conform as well as possible to our current understanding of the laws of physics.
The following is how I envisage one kind of minefield to be in space.
At the centre of every minefield is a type of entity called a caretaker. Surrounding the caretaker are the mines that the caretaker is in charge of.
The mines will be laid out around the caretaker using a particular layout. The layout that the mines adopt are configurable, and can be changed using the user interface. In the UI, the minefield is displayed as a graph of nodes, where each node represents a mine. Changing the layout of the nodes in the graph then directly corresponds to changing the layout of the mines in the minefield. This would fit in perfectly with the work Josh has already done, as seen here (19:43).
Three examples of possible layouts are:
- Cubic - The minefield is divided into sectors of equal volume, each one a cube with eight mines forming the vertices. The distances between mines are all equal.
- Hexagonal lattice - Mines are divided into layers along one axis, and each layer consists of a tessellating arrangement of hexagons along the other two axes. Mines are positioned at the vertices of these hexagons. Think of graphene!
- Spherical - The mines are arranged into football-like structures that approximate a sphere. This arrangement is non-tessellating.
That being said, everything else in this suggestion is only included because it's necessary. For the remainder of the suggestion, I assume the minefield layout to be cubic, as shown below. In this layout, a sector is defined to be a cubic volume of space within the minefield bounded by 8 adjacent mines.
Figure 1: Top, front and side view of minefield with cubic arrangement
The caretaker is the entity at the centre of the minefield that provides the following functions:
- It manipulates the positions and velocities of all of the mines within the minefield.
- It provides maintenance to all mines within the minefield.
- It passively scans for hostiles entering the minefield.
Next to the generator is the computer core, which is a relatively powerful array of processors that drain a small fraction of the power from the generator and carries out the following kinds of computation:
- It receives and processes information from the passive sensor suite lining the outer shell (see below).
- If a hostile is detected, it calculates the velocity vector of the hostile.
- When a hostile's velocity vector is calculated, it computes the trajectories of nearby mines necessary to intercept it.
- When the trajectories of mines are calculated, it works out the appropriate vectors to beam electrons and/or positrons along (see below).
- It controls the other components: the generator, the positronium containment compartments and the positronium separators (see below).
The purpose of positronium production and storage is that it acts as both a battery and a buffer storage for electrons and positrons in case the generator cannot produce them fast enough. Positrons and electrons would be difficult to store separately as a group of each stored separately would generate strong electric repulsive forces even in small quantities, and hence would require a lot of energy to contain. Although positronium is typically very unstable, there are existing proposals for making it far more stable, by converting it into a Bose-Einstein Condensate state or through the use of crossed electric and magnetic fields.
The caretaker is able to power, relay information and control the position and velocity of mines by beaming electrons towards them. To do this, electrons from the generator (or from the dissolution of positronium) are channeled into one of the emitters on the outer shell and accelerated as a beam towards the appropriate mines. For each mine, one beam of electrons is beamed directly at the mine and is used to relay information and provide power. The other beam is directed towards the very local vicinity of the mine, and the mines are able to use electromagnets to produce a Lorentz force on this beam to affect their velocity vector (see: Positron Mine).
Figure 2: Schematic representation of minefield caretaker (full image here)
The positron mine is a 1kg explosive device containing a 1 mg (milligram) positronium payload. It maintains the positronium in a stable configuration until it receives a signal to detonate, at which point it allows the positronium to collapse into positrons and electrons, which annihilate with each other releasing 9.0*10^10 joules (90 gigajoules) of energy.
The positron mine has limited automatic functionality relative to the caretaker. It is unable to move by itself, unless in the presence of electrically charged objects. It has no sensor equipment and therefore has no knowledge of its surrounding environment. In normal operation it remains dormant and is extremely hard to detect at any distance beyond close range.
Like the caretaker, the outer shell of the mine is constructed out of meta-materials, enhancing its stealth. Instead of emitters, the casing of each mine is lined with channels that can receive an incoming stream of electrons or positrons for the purposes of information transfer, energy transfer, energy storage and payload replenishment. The stream of electrons can be decelerated in a generator to produce power and can also be deciphered by a microprocessor to obtain information (see below).
Behind the casing is an array of electromagnets. These electromagnets are used to generate electric fields around the mine that can be used for two purposes.
- They can be used to generate a Lorentz force on streams of electrons and positrons, which in turn will produce a force on the mine itself (Newton's third law) that can be used to accelerate it towards hostiles, allow it to reposition itself in conformity with a new layout, or return to the caretaker for maintenance.
- When in close proximity to a hostile ship with a hull made of a ferrous material, they can help guide the mine towards the ship with reduced or zero assistance needed from the caretaker (except possibly to continue to provide power).
When the caretaker beams electrons and positrons to the mine, it does so in a way that conveys information. The mine's microprocessor deciphers this information from the incoming electron and positron streams to determine the electric fields that the electromagnets should produce and to know when it should detonate. The following message protocol is used:
In the stream of electrons or positrons, each potential particle that could arrive corresponds to one bit of information. If a particle actually does arrive, this corresponds to bit state 1; if no particle arrives in that moment, it corresponds to bit state 0. Each byte (8 bits) of information is delineated with bit state 1. The assumption is made that each mine will require 1 MB/s information transfer rate when active to pursue a hostile. To satisfy this contraint, the caretaker will need to transmit between 1,000,000 and 9,000,000 electrons or positrons per second to the mine. The delineation between bytes is necessary for two reasons: to maintain synchronisation during data reception, and to guarantee a lower bound to the number of accelerated particles that the mine receives per second, and hence power. Since each potential particle conveys only 1 bit of information, the bit rate is equivalent to the baud rate.
Figure 3: Schematic representation of positron mine (full image here)
Complex Caretaker-Mine Interactions
When a hostile is detected by the caretaker, it will need to direct mines towards it. However, in certain layouts the direct path between the caretaker and a mine may be blocked by other mines. The diagram below demonstrates how the caretaker may use additional mines as relays to provide information, power and momentum to the mines it intends to move.
Figure 4: Demonstration of how mines may serve as relays between the caretaker and other mines
A diagram illustrating the current estimate of the relative scale of the caretaker to a mine is given below.
Figure 5: Relative size of caretaker to a mine
The mathematics used to assess the feasibility of this design is given in rough below.
Note that these calculations are rough and likely to be incorrect. From these calculations:
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CONSTANTS ------------------------------- Speed of light, c = 3.00*10^8 ms^-1. Rest mass of electron, m[electron] = 9.11*10^-31 kg. Charge of an electron = q[electron] = 1.60*10^-19 C. ASSUMPTIONS ------------------------------- Assume uniform minefield encompassing volume 1000km*1000km*1000km. Assume 1000 mines within the minefield. Distance between mines = ( (1000 / (1000)^(-1/3)), (1000 / (1000)^(-1/3)), (1000 / (1000)^(-1/3)) ) = ( 100km, 100km, 100km ) = 100 km in x, y and z dimensions. Define [b]sector[/b] to be a region in the minefield bounded by six adjacent mines. Volume of a sector = 100km*100km*100km. Assume mass of each mine = 1kg. Assume minefield setup is classified as successful if and only if a mine can reach a target entering a sector it bounds before the target leaves the sector. Assume setup is specified to be successful for targets travelling up to 1000 ms^-1. Assume caretaker needs to provide information to an active mine at 1 MB/s. Assume caretaker needs to provide power to an active mine at 1 MJ/s (1 MW). Assume maximum power output of caretaker is 1 GW. Assume maximum energy capacity of caretaker is 10000 GJ = 10 TJ. Assume message protocol using positronium with 1 baud = 1 bit. Assume maximum permissible electron / positronium stream delay from central caretaker of minefield to most distant mine = 1s CALCULATIONS ------------------------------- Consider worst case: Target T enters a sector travelling at a constant velocity of 1000 ms^-1 parallel to one of the axes (e.g. x axis) and along the centre of the sector in the other two axes (e.g. y and z). Time for T to cross sector = 100*10^3 / 1000 = 100 seconds. Distance of closest mine to target as it exits sector = ((50*10^3)^2 + (50*10^3)^2)^0.5 = 70710 metres. Assume mine is initially stationary and will need to accelerate at a constant rate to intercept target. Acceleration needed: v = unknown u = 0 s = 70710 a = ? t = 100 s = ut + 0.5at^2 s = 0.5at^2 a = 2*s*t^-2 a = 2*70710*0.0001 a = 14.1 ms^-2 Acceleration needed by closest mine to intercept target is 14.1 ms^-2. Force needed by closest mine to intercept target = m*a = 1*14.1 = 14.1 N. Maximum distance from centre of minefield to most distant mine = ((500*10^3)^2 + (500*10^3)^2)^0.5 = 707,106 metres. Electron velocity = d / t = 707106 / 1 = 707106 ms^-1. Bit rate = baud rate from caretaker to mine = 1 MB/s Use message protocol: 1 potential electron = 1 baud / bit Electron present = 1, electron absent = 0 Delineation between bytes requires 1 electron. 1 MB/s --> 1,000,000 electrons/s + 8,000,000 potential electrons/s Message with all 0's: 1,000,000 electrons/s Message with all 1's: 9,000,000 electrons/s Constraints on number and velocity of electrons. 1. Maximum power output of caretaker for production/acceleration of electrons = 1GW. 2. Electrons must be able to cross minefield in 1s -> v[electron] >= 707106 ms^-1. 3. Electrons should not accelerate past 0.1c -> v[electron] <= 30,000,000 ms^-1 4. Active mine needs 1 MB/s data feed -> N >= 9,000,000. 5. Active mine needs 1 MW of power -> 0.5*N*m[electron]*(v[electron]^2) > 1,000,000 Energy to produce electron = 2*m[electron]*c^2 = 2*(9.11*10^-31)*(3.0*10^8)^2 = 1.64*10^-13 J. From constraint 3 and 5: N*0.5*(9.11*10^-31)*((3*10^7)^2) > 1,000,000 N > 1,000,000 / (0.5*(9.11*10^-31)*((3*10^7)^2)) N > 2.4393219*10^21 Take N = 10^22, V = 30,000,000 ms^-1 Energy to produce 10^22 electrons = 10^22 * 1.64*10^-13 J = 1.64*10^9 J. Energy to accelerate 10^22 electrons to V = 0.5*N*m[electron]*(v[electron]^2) = 0.5*10^22*(9.11*10^-31)*(3*10^7)^2 = 4.10*10^6 J. Total energy to produce N electrons and accelerate them to V = 1.64*10^9 J + 4.10*10^6 J = 1.64*10^9 J (acceleration component is insignificant). Total power required = energy required / second = 1.64*10^9 W. Satisfies constraints? 1. Total power output of caretaker = 1GW. 2. Total power required = 1.64 GW. 3. Total energy capacity of caretaker = 1000 GJ. Time of depletion of battery at max capacity with max power usage = 1000 / (1.64*10^9 - 1*10^9) = 1000 / 0.64 = 1562.5 seconds It only takes 100 seconds to intercept target. Constraint 1: satisfied. Velocity of electrons = 30,000,000 ms^-1. Velocity lower bound = 707106 ms^-1. Velocity upper bound = 30,000,000 ms^-1. Velocity upper bound >= velocity of electrons >= velocity lower bound. Constraint 2: satisfied. Constraint 3: satisfied. Number of electrons produced / s = 10^22. Number of electrons required for 1 MB/s data transmission = 9*10^9. 10^22 > 9.10^9 Constraint 4: satisfied. Power provided = 0.5*N*m[electron]*(v[electron]^2) / 1 = 0.5*10^22*(9.11*10^-31)*(3*10^7)^2 / 1 = 4.10*10^6 W. Energy required = 1*10^6 W. 4.10*10^6 > 1*10^6 Constraint 5: satisfied. At maximum operation, the caretaker produces 10^22 electrons and accelerates them to 30,000,000 ms^-1 (0.1c). The change in momentum of the mine is produced by causing a change in momentum of the electron stream. These changes in momentum must be equal in magnitude (conservation of momentum). d(Momentum) = F*dt, let dt = 1: d(Momentum) = F = 14.1 kgms^-1 Change in momentum of each electron = 14.1 / 10^22 = 1.41*10^-21 kgms^-1 Relativistic momentum = m0*v*(1 - v^2/c^2)^-0.5 Substituting for v, v = 0.98c = 293,796,609 ms^-1 The mine's electromagnetic field will need to cause a change of velocity of 0.98c for 10^22 electrons in one second to generate the necessary change in its momentum of 14.1 kgms^-1. Using V = (gamma - 1)*m[electron]*c^2 / q[electron]: V = (5.025 - 1)*(9.11*10^-31)*(3.0*10^8)^2 / (1.60*10^-19) = 2.06*10^6 V. The mine may need to generate ~2,060,000V to accelerate electrons at this velocity. If the energy generated by slowing electrons beamed from the caretaker (4.10*10^6) is insufficient to produce this voltage, the electrons can instead be annihilated with a portion of the mine's positron payload for vastly increased energy. The positron payload can be refilled by the caretaker simply by beaming positrons rather than electrons to the mine.
- A 1 kg mine will require 14.1 N of force to accelerate sufficiently fast (14.1 ms^-2) to intercept a hostile target travelling at 1000 ms^-1 through one of its designated sectors in the worst-case situation.
- The caretaker will need to produce and emit 10^22 electrons (or positrons) per second at a velocity of 0.1c towards the mine. Most of these will be beamed to the local vicinity of the mine so that the mine can produce a Lorentz force on them to alter its own momentum. To alter its momentum sufficiently fast for a 14.1 ms^-2 acceleration, it will need to change the velocity of the particle stream by 0.98c. The necessary electric field may require 2,600,000 V to cause this change in velocity, although this was calculated assuming a uniform, linear electric field when in reality the mine would produce a radial electric field. This is roughly the same voltage as a powerful taser gun. The current required (and therefore power) is uncalculated.
- It is assumed that the mine requires 1 MJ/s (1 MW) of power and 1 MB/s of data input. A small fraction (24.4%) of electrons output by the caretaker are directed straight towards the mine for these purposes.
 Transforming Light (http://docs.lib.purdue.edu/cgi/viewcont ... xt=nanopub)
 High Density Storage of Excited Positronium using Photonic Bandgap Traps (http://www.google.com/patents/EP1652194B1)
 Propulsion and Power with Positrons (http://www.niac.usra.edu/files/library/ ... enneth.pdf)
So what do you guys think?
Edit: Just_Ice_au, I dare you to link old posts and tell me that this has been even remotely explored before.
Edit 2: Accidentally was working with assumption that mines were 10 kg each. Updated maths.
Edit 3: Corrected payload from 1 ug (microgram) to 1 mg (milligram). I'm not going to alter this in the schematics since this would take time, but just be aware that the payload is meant to be in milligrams now.