From: Amara Graps (amara@amara.com)
Date: Sat Aug 17 2002 - 07:51:10 MDT
Avatar Polymorph:
>>Nine atoms of anti-hydrogen were
>> produced just over a year ago. Now, the new factory will produce them at a
>> rate of more than 2,000 atoms per hour, Close said.... 1998]
Anders Sandberg:
>I would be surprised if no Sandia or DoE engineers have ever thought
>about it, maybe even written some memos about it, but it is unlikely
>there has been any serious work. Antimatter is enormously more costly
>than plutonium,
There _has_ been some serious work using anti-protons to test
Einstein's Equivalence Principle, but the project at Los Alamos ran
out of money, last I heard (maybe because producing the antiproton
was expensive ?!?) Sad, because this project was really a clever
idea.
----------------------
References:
R. E. Brown, J. Camp, T. Darling, P. Dyer, T. Goldman, D. B.
Holtkamp, M. H. Holzscheiter, R. J. Hughes, N. Jarmie, R. A.
Kenefick, N. S. P. King, M. M. Nieto, D. Oakley, R. Ristinen, and F
C. Witteborn, ``A Measurement of the Gravitational Acceleration of
the Antiproton: A Status Report," Los Alamos Internal Report, (1990
unpublished).
Jarmie, Nelson (1987), "A Measurement of the Gravitational
Acceleration of the Antiproton: An experimental Overview," Nuclear
Instruments and Methods in Physics Research B24/25, pp. 437-441.
Goldman, Terry, Hughes, Richard, Nieto, Michael, (1988), "Gravity
and Antimatter", Scientific American, March 1988, pp. 48-56.
Dicke, R.H. (1961), "The Eotvos Experiment", Scientific American,
pp. 84-94.
Fred C. Witteborn, ``Free Fall Experiments with Negative Ions and
Electrons," Ph.D. thesis, Stanford University, 1965.
Fred C. Witteborn and William M. Fairbank, ``Apparatus for Measuring
the Force of Gravity on Freely Falling Electrons," Rev. Sci.
Instrum. {48}, 6 (Jan 1977).
(F.C. Witteborn was one of my MS thesis advisors.)
----------------------
I earned my MS Physics degree 11 years ago, by simulating one part
of this experiment. If any of you are interested in numerical
techniques for Nbody methods (here: particle-particle method),
you might like the paper.
Work on that project is here:
http://www.amara.com/past/particles.html
"Investigating the Motions and Energies of Ions Confined in a
Uniform Magnetic Field" Full Text: PDF (1.4Mb)
http://www.mpi-hd.mpg.de/dustgroup/~graps/msthesis/MSThesis.pdf
(individual PDFs of chapters below)
ABSTRACT
The research described in this thesis is aimed at understanding
the motion and energies of charged particles trapped in a constant
magnetic field B. The study entailed writing a computer simulation
of the motion of three ions confined in a constant, vertical
B-field. While the simulation is general enough to allow n charged
particles of any charge and mass, the cases constructed were only
for hydrogen ions. Computed quantities for the ions included
positions, velocities, kinetic and total energies.
The calculated positions and velocities elucidate how a system of
three charged particles behave under the classical assumption of
the Lorentz force. We were especially interested in the variation
with particle density of the kinetic energy exchange (coupling)
between the energy related to motion parallel to and orthogonal to
the confining magnetic field. It is found that as the density of
the three particle system decreases, the coupling decreases.
CONTENTS
1:Introduction{1}
2:Physical Theory{5}
2.1 Force Equations{5}
2.2 Gyroscopic Radius{6}
2.3 Gyroscopic Period{8}
2.4 Relationship between KE and B-field{8}
2.5 Relationship between T_z and t_max{12}
2.6 Cooling of Accelerating Particles{15}
3:Integration Algorithms{19}
3.1 Setting up the Equations of Motion {19}
3.2 The Verlet Algorithm{20}
3.3 The Runge-Kutta 4 Algorithm{21}
3.4 The Bulirsch-Stoer Algorithm{22}
3.5 Comparison of Integration Methods{25}
4:Variable Time Step Algorthms{27}
5:The Program: Colliding Ions {31}
6:Results{33} Chapt. 6 (PDF)
6.1 Motion{36}
6.2 Gyroscopic Radius{37}
6.3 Gyroscopic Period {53}
6.4 Rotational Kinetic Energy{56}
6.5 Vertical Kinetic Energy{57}
7:Conclusions{59}
Appendices (61)
A. Verlet Derivation{61}
B. Source Program Colliding Ions{65}
C. Example Input File CollidingIonsIn.text(99}
Bibliography {101}
(Web Page Introduction)
In 1991, I completed my master's thesis project simulating charged
particles trapped in a magnetic field. The goal was to understand
the particles' motion and energies. In turn, I would provide
supplementary kinetic energy information to a group of
experimenters at Los Alamos who were trying to measure the Earth's
gravitational effect on antiprotons in a uniform magnetic field
using the "time-of-flight" (TOF) method.
Question: Why would one care about the Earth's gravitational effect
on antiprotons?
Answer: The equivalence principle of Einstein's general theory of
relativity states that the ratio of gravitational mass to inertial
mass is unity for all materials, even antimatter. The equivalence
principle has been verified to better than one part in 10^11 for
neutral matter, but has not been fully verified for charge
constituents of neutral matter (i.e. protons, anti-protons,
electrons etc.). If a different gravitational force is found for
charged particles, then the equivalence principle would be
violated, and the general theory of relativity would have to be
re-examined.
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-- *********************************************************************** Amara Graps, PhD email: amara@amara.com Computational Physics vita: ftp://ftp.amara.com/pub/resume.txt Multiplex Answers URL: http://www.amara.com/ *********************************************************************** "The universe: a device contrived for the perpetual astonishment of astronomers." -- Arthur C. Clarke
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