Editing Antimatter rocket (section)

==Difficulties with antimatter rockets==
The chief practical difficulties with antimatter rockets are the problems of creating antimatter and storing it. Creating antimatter requires input of vast amounts of energy, at least equivalent to the rest energy of the created particle/antiparticle pairs, and typically (for antiproton production) tens of thousands to millions of times more.<ref>{{cite web|title= Laser Pulse Produces Positrons |url= http://www.photonics.com/Article.aspx?AID=35682 |date=2008-11-18|publisher= Photonics Media |access-date=2008-11-18<!--DASHBot-->}}</ref><ref>{{cite journal|doi=10.1103/PhysRevLett.102.105001|pmid=19392120|title=Relativistic Positron Creation Using Ultraintense Short Pulse Lasers|date=2009|author=Chen, Hui|journal=Physical Review Letters|volume=102|pages=105001–105004|last2=Wilks |first2=Scott C. |last3=Bonlie |first3=James D. |last4=Liang |first4=Edison P. |last5=Myatt |first5=Jason Myatt
|last6=Price |first6=Dwight F.  |last7=D. Meyerhofer |first7=David D. |last8=Beiersdorfer |first8=Peter  |issue=10|bibcode=2009PhRvL.102j5001C|url=https://zenodo.org/record/1233811}}</ref> Most storage schemes proposed for interstellar craft require the production of frozen pellets of antihydrogen. This requires cooling of antiprotons, binding to positrons, and capture of the resulting antihydrogen atoms - tasks which have, {{As of|2010|lc=on}}, been performed only for small numbers of individual atoms. Storage of antimatter is typically done by trapping electrically charged frozen antihydrogen pellets in [[Penning trap|Penning]] or [[Quadrupole ion trap|Paul trap]]s. There is no theoretical barrier to these tasks being performed on the scale required to fuel an antimatter rocket. However, they are expected to be extremely (and perhaps prohibitively) expensive due to current production abilities being only able to produce small numbers of atoms, a scale approximately 10<sup>23</sup> times smaller than needed for a 10-gram trip to Mars.

{{Anchor|effecient2016-01-30}}Generally, the energy from antiproton annihilation is deposited over such a large region that it cannot efficiently drive nuclear capsules.  Antiproton-induced fission and self-generated magnetic fields may greatly enhance energy localization and efficient use of annihilation energy.<ref>{{cite journal|last=Solem|first=J. C.|year=1991|title=Prospects for Efficient Use of Annihilation Energy|journal=Fusion Technology|volume=20|issue=4P2 |pages=1040–1045|doi=10.13182/FST91-A11946978 |bibcode=1991FuTec..20.1040S |osti=6628569}}</ref><ref>{{cite journal|last1=Augenstein |first1=B. W.|last2=Solem|first2=J. C.|year=1990|title=Antiproton initiated fusion for spacecraft propulsion |journal=Report ND-3555-SDI (The RAND Corporation, Santa Monica, CA)}}</ref>

A secondary problem is the extraction of useful energy or momentum from the products of antimatter annihilation, which are primarily in the form of extremely energetic [[ionizing radiation]]. The antimatter mechanisms proposed to date have for the most part provided plausible mechanisms for harnessing energy from these annihilation products. The classic [[Tsiolkovsky rocket equation|rocket equation]] with its "wet" mass (<math>M_0</math>)(with [[propellant mass fraction]]) to "dry" mass (<math>M_1</math>)(with [[Payload fraction|payload]]) [[Mass ratio|fraction]] (<math>\frac {M_0}{M_1}</math>), the velocity change (<math>\Delta v </math>) and specific impulse (<math>I_{\text{sp}}</math>) no longer holds due to the mass losses occurring in antimatter annihilation.<ref name=AIAA-2003-4696/>

Another general problem with high powered propulsion is excess heat or [[waste heat]], and as with antimatter-matter annihilation also includes extreme radiation. A proton-antiproton annihilation propulsion system transforms 39% of the propellant mass into an intense high-energy flux of gamma radiation. The gamma rays and the high-energy charged pions will cause heating and radiation damage if they are not shielded against. Unlike neutrons, they will not cause the exposed material to become radioactive by transmutation of the nuclei. The components needing shielding are the crew, the electronics, the cryogenic tankage, and the magnetic coils for magnetically assisted rockets. Two types of shielding are needed: [[radiation protection]] and [[cold shield|thermal protection]] (different from [[Heat shield]] or [[thermal insulation]]).<ref name=AIAA-2003-4696/><ref name=Forward1985>[http://arc.aiaa.org/doi/abs/10.2514/3.22811 ''Antiproton Annihilation Propulsion''] R. L. Forward, September 1985</ref>

Finally, relativistic considerations have to be taken into account. As the by products of annihilation move at [[Special relativity|relativistic velocities]] the [[Mass in special relativity|rest mass changes]] according to [[mass–energy equivalence|relativistic mass–energy]]. For example, the total mass–energy content of the neutral pion is converted into gammas, not just its rest mass.  It is necessary to use a [[Relativistic rocket#Relativistic rocket equation|relativistic rocket equation]] that takes into account the relativistic effects of both the vehicle and [[Working mass|propellant exhaust]] (charged pions) moving near the speed of light. These two modifications to the two rocket equations result in a mass ratio (<math>\frac {M_0}{M_1}</math>) for a given (<math>\Delta v </math>) and (<math>I_{\text{sp}}</math>) that is much higher for a relativistic antimatter rocket than for either a classical or relativistic "conventional" rocket.<ref name=AIAA-2003-4696/>

===Modified relativistic rocket equation===
The loss of mass specific to antimatter annihilation requires a modification of the relativistic rocket equation given as<ref name=AIAA-98-3403>[http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/20238/1/98-1132.pdf ''Evaluation of Propulsion Options for Interstellar Missions''] {{webarchive|url=https://web.archive.org/web/20140508061651/http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/20238/1/98-1132.pdf |date=2014-05-08 }} Robert H. Frisbee, Stephanie D. Leifer, AIAA Paper 98-3403, July 13–15, 1998.</ref>

{{NumBlk|:|<math>\frac {M_0}{M_1} = 
\left(\frac{1+ \frac{\Delta v}{c}}{1- \frac{\Delta v}{c}}\right)^{\frac{c}{2 I_{\text{sp}}}}
</math>|{{EquationRef|I}}}}

where <math>c</math> is the speed of light, and <math>I_{\text{sp}}</math> is the specific impulse (i.e. <math>I_{\text{sp}}</math>=0.69<math>c</math>).

The derivative form of the equation is<ref name=AIAA-2003-4696/>

{{NumBlk|:|<math>\frac {dM_{\text{ship}}}{M_{\text{ship}}}=
\frac {-dv ( 1 - I_{\text{sp}} \frac {v}{c^2})}
{(1 - \frac {v^2}{c^2})(-\frac {I_{\text{sp}} v^2}{c^2} +  (1 - a) v + a I_{\text{sp}})}
</math>|{{EquationRef|II}}}}

where <math>M_{\text{ship}}</math> is the non-relativistic (rest) mass of the rocket ship, and <math>a</math> is the fraction of the original (on board) propellant mass (non-relativistic) remaining after annihilation (i.e., <math>a</math>=0.22 for the charged pions).

{{EquationNote|Eq.II}} is difficult to integrate analytically. If it is assumed that <math>v \sim I_{\text{sp}}</math>, such that <math>(1 - \frac {I_{\text{sp}} v}{c^2}) \sim (1 - \frac {v^2}{c^2})</math> then the resulting equation is

{{NumBlk|:|<math>\frac {dM_{\text{ship}}}{M_{\text{ship}}}=
\frac {-dv}{(-\frac {I_{\text{sp}} v^2}{c^2} + (1 - a) v + a I_{\text{sp}})}
</math>|{{EquationRef|III}}}}

{{EquationNote|Eq.III}} can be integrated and the integral evaluated for <math>M_0</math> and <math>M_1</math>, and initial and final velocities (<math>v_i = 0</math> and <math>v_f = \Delta v</math>).
The resulting relativistic rocket equation with loss of propellant is<ref name=AIAA-2003-4696/><ref name=AIAA-98-3403/>

{{NumBlk|:|<math>\frac{M_0}{M_1}=\left(\frac{(-2I_{\text{sp}}\Delta v/c^2+1-a-\sqrt{(1-a)^2+4aI_{\text{sp}}^2/c^2})(1-a+\sqrt{(1-a)^2+4aI_{\text{sp}}^2/c^2})}{(-2I_{\text{sp}}\Delta v/c^2+1-a+\sqrt{(1-a)^2+4aI_{\text{sp}}^2/c^2})(1-a-\sqrt{(1-a)^2+4aI_{\text{sp}}^2/c^2})}\right)^{\frac{1}{\sqrt{(1-a)^2+4aI_{\text{sp}}^2/c^2}}}
</math>|{{EquationRef|IV}}}}

===Other general issues===

The cosmic background [[hard radiation]] will ionize the rocket's hull over time and poses a [[Health threat from cosmic rays|health threat]]. Also, gas plasma interactions may cause [[space charge]]. The major interaction of concern is differential charging of various parts of a spacecraft, leading to high electric fields and arcing between spacecraft components. This can be resolved with well placed [[plasma contactor]]. However, there is no solution yet for when plasma contactors are turned off to allow maintenance work on the hull. Long term space flight at interstellar velocities causes erosion of the rocket's hull due to collision with particles, [[Interstellar medium|gas]], [[Cosmic dust|dust]] and [[micrometeorite]]s. At 0.2<math>c</math> for a 6 light year distance, erosion is estimated to be in the order of about 30&nbsp;kg/m<sup>2</sup> or about 1&nbsp;cm of aluminum shielding.<ref name=NASA20110406>[https://web.archive.org/web/20110621012238/http://science1.nasa.gov/science-news/science-at-nasa/2001/ast13nov_1sidebar/ ''Space Charge''] NASA science news, April 6, 2011</ref><ref name=HGarrett>[http://www.kiss.caltech.edu/workshops/systems2012/presentations/garrett.pdf ''There and Back Again: A Layman's Guide to Ultra-Reliability for Interstellar Missions''] {{webarchive|url=https://web.archive.org/web/20140508062130/http://www.kiss.caltech.edu/workshops/systems2012/presentations/garrett.pdf |date=2014-05-08 }} Henry Garrett, 30 July 2012</ref>