Dream for the Stars or at least way to store anti-matterstatic.sif.it/SIF/resources/public/files/va2009/lynn_0714a.pdf · Dream for the Stars or at least way to store anti-matter

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Dream for the Stars or at least way to store anti-matter

Fermi School - Varenna, July 2009

Acknowledgements Current: •  K Lynn M Weber L Pilant Joshah Jennings

Students: Jia Xu John Cox(undergraduate) D Solodovnikov

•  John Bumgarner –SRI (MEMS Technology)

Former Team Members: •  A Hunt (ISU) •  S McNeil( graduate student) •  D. Cassidy –has moved on to BEC and annihilation lasers

Recent and Past support (for the accelerator): •  WM Keck Foundation •  SMDC •  DOE


Outline •  Why? Highest energy density •  How?

•  Making antimatter (positrons) •  Bottles for antimatter •  Filling the bottle (trap) •  Storage and release

•  Roadmap •  Beyond proof of concept… •  Particle optics before plasmas


Outline •  We need to develop out of the box

methods to store the maximum number of anti-matter that can be used at a later time for various applications.

•  Our work is not similar of Surko and team. Multi-Cell is an extension of Greaves & Surko previous work.

•  We plan to use small diameter, and long aspect ratio traps and their multi-cell trap.


Why store antimatter?

Reaction / source of energy

Specific energy (J/kg)

Fraction used For energy

Antimatter (e.g. positrons) Plus matching mass of

matter

1.8· 1017 100%

Fusion of deuterium-tritium 3·1014 0.34%

Fission of 235U 8·1013 0.09 %

TNT 5·106 7 ·10-9 %


Current moderation scheme

1 x10-3 of positrons used


Conclusion need moderated positrons to realistically store

•  “Most cost effective” means to create antimatter

•  However it does costs energy to produce but can use as stored energy

•  Portable positron sources without the need of radioactive sources could be used research and industry.

•  Need to have a method to store macroscopic amounts.- Need new ideas>>>>> Fermi School -

Varenna, July 2009

Plasma is a distinct phase of matter, separate from the traditional solids, liquids, and gases. It is a collection of charged particles that respond strongly and collectively to electromagnetic fields, taking the form of gas-like clouds or ion beams. Since the particles in plasma are electrically charged (generally by being stripped of electrons), it is frequently described as an "ionized gas.”

Space charge is the excess of electrons or ions in a given volume.

Definitions :::

Deviation for Coulomb Potential

Shielding is a collective behavior inside a Debye sphere of radius, λ D with sphere contaiing enough particles?

Volume of sphere = (4π/3) ne *λ3 D = Λ plasma parameter

ne *λ3 D = Λ >> 1

Suggesting the mean PE of a particle due to its nearest neighbor is inversely proportional to the to the mean inter particle distance α ne

1/3 must be << kb T

Brief Review of traps •  Van Dyck et al (Dehmelt) modified Penning trap stores a single

positron for 111 days (PRL 59, 26 (1987))

•  Liquid He cooled superconducting magnet around Penning quadruple trap (K Blaum Phys Reports 425, 1 (2006) –  B-field as high as 9 Tesla –  B-field homogeneous 1 in 108 per cm3 –  B-field time stable 1 in 109 per hour; –  4 K vacuum system: 10-16 torr pressure or on the order of 100

atoms per cm3 –  Hydrogen vapor pressure at 4 K: 10-7 torr or 1011 atoms/cm3. –  Single charged particle!

Fermi School- Varenna July 2009

Review ( Surko contribution) •  Surko trap for positrons (Surko PRL 62, 901

(1989)): – 3.3×105 positrons in 12 cm3; – Density = 2×104 /cm3. – 0.086 Tesla field, 1.5×10-6 Torr – Confinement times 60 sec: dependent on

pressure – Efficient cooling of positrons from ~1 eV to 3/2

kT in <3 sec


Review •  Surko trap (Greaves PRL 75, 3846 (1995))

– 0.126 Tesla; 5×10-10 Torr – 2.0×107 positrons in 1.5 radius by 20 L (cm); –  Density 3×105 /cm3; Δ= 0.025 eV

•  Current trap: (Surko talk at summer school) – 4.8 Tesla, 4×108 e+,density –  1 x 109 / cm3 – Lifetime ~1500 s

•  Surko plans: Presented during the first week of the summer school 1010 positrons and more with multi-cell>>>> Fermi School-

Varenna July 2009

Trapping: Old School

New School? Fermi School - Varenna, July 2009

Standard Trap •  Current state: Malmberg-Penning (MP) trap

–  Developed for high energy plasma physics –  Goal: study physics at high density/temperatures

•  MP trap: axial B-field, E-field at end caps –  Single large trap –  High temperature and density? New idea –  Large confining potentials –  Densities approaching Brillouin limit –  Significant radial motion across B-field lines –  Rotating walls used in high densities


A Bottle for antimatter •  No contact with the walls-positron:

–  Electric and magnetic fields •  Little matter within the bottle:

–  Excellent vacuum( < 10-10 torr) –  Can use cold environment- cool by

radiation not clear for small diameter •  Malmberg-Penning (PM) traps

–  Magnetic radial confinement –  Electric axial confinement


How? •  “Moderate” to make usable for trapping

•  New SiC field assisted moderators are being developed to increase efficiency 10 times to ~10%

•  Trap into Traps-Stop throwing e+ away? •  Long narrow traps reduce charge pressure or voltage on

end walls •  Multiple traps shield trapped positrons in traps from each

other •  Special moderator design aligned with micro trap •  May need to use rotating wall if dimensionally scale


Penning-Malmberg traps


+ - + -

Malmberg Penning Trap

Cylinder trap

End cap End cap

Positrons

Magnetic field resists radial drift Electric field -stops axial escape

E E

B

End cap potential needs to reflect and overcome space charge

Particle-particle scattering and inhomogeneous end fields cause radial drift and potential loss

Annihilations with electrons in residual gas


Malmberg-Penning Trap Confinement B-Field Radial and E-Field Axial

•  Typical Plasmas- No Rotating wall –  L≈10 cm d > 2 cm –  B ≈ 1 kG to 5 T; V≈10 V to 10 kV

•  Non-Interacting Particle Trajectories –  Axial Direction: Harmonic Like Motion –  Radial Direction: Cyclotron and Magnetron Motion

V+ V+ e+ Plasma

B-Field


The outline of the modeling our setup- Lecture III

The upper half of the positron trap, ABN and EDC are applied 10V, other boundaries are grounded


Parameters •  rt and rp radius of trap and plasma •  Lt and Lp length of trap and plasma •  ρ and V are density of positrons and volume of

plasma •  mc2 =mass of particles (c speed of light) •  q = charge of particles •  B and U magnetic field and end cap potential •  Ro n Zeff are electron radius, gas density and

effective number of electrons per molecule •  p = pressure in trap


B-Field Energy Equals Plasma’s Rest Mass Energy

•  Total B-Field Energy Greater in Real Trap

•  Rearrange Brillouin Limit Equation (CGS Units)

B-Field Energy Density

Plasma’s Rest Mass Energy Density


Maximum Plasma Density Set by Radial Confinement •  Two Counter Acting “Forces” Simple Trap

–  Space Charge Pushes Plasma Towards Trap Walls

–  B-Field Pushes Plasma Towards Axis

•  At Brillouin Limit “Forces” Balance

–  Maximum Achievable Density

• 

–  nmax = 2 × 1013 cm-3 for B = 2 T –unrealistic

•  Independent of Total Particle Number

–  Build Bigger Traps?

rb

FB

B

Trap Wall

Plasma


One now knows when fluids are used in small diameter tubes the flow is not turbulent but is laminar a surprise to everyone. Now it is now being understood in the last 10 years?

Does this happened for plasmas????? Are Plasmas like fluids like stated in the articles?

Changing dimensions produces surprises For those that do not want to check 60 years of work: Note that in microchannel flow switch for solutions and gases somehow solved impossible separations when changed to different dimensions ?

Space Charge Limits Total Number of Stored e+

•  Long Plasma Manageable? •  Needed Axial Potential is Problematic

–  V = 1.3 kV at 1011 e+ –  V = 100 kV at 1013 e+

L = 34 cm dp= 0.68 cm dw= 1.36 cm

€

V =eN+

L1+ 2ln rw

rp


Micro-traps

Long narrow traps: less force required to Hold positrons (of equal charge) together: Tall narrow water tank vs. shallow wide tank

Many traps vs. one: metal matter dividers between traps screen the charges as Faraday pointed out and do not “see” each other? Isn’t this obvious? Less force required to hold them when screened just like solids. The end cap potential is measured in volts rather than kilovolts. Fermi School -

Varenna, July 2009

Space charge potential developed in micro Malmberg-Penning trap array (solid line) compared to a large standard trap (dashed line). The space charge potentials are calculated from equation and are for a cylindrical plasma confined by cylindrical electrodes.

The plasma dimensions for the micro trap are

rp=rw/2=12.5 microns, L=10 cm

Norma trap:

rp=rw/2 ~ 10000 microns L=117 cm.

The point is plasma physics have never tested this regime for 60 years and have not stated in the literature that it would not work???

Changing dimensions produces surprises

If one assumes that the misalignment of the tube should be within the size of a cyclotron radius (i.e. 0.34 µm) The misalignment should be no more than 7 arc seconds from particle optics. Technically challenging

5 µm diameter (present plans 100 µm) Fermi School - Varenna, July 2009

The modeling of crossed-field electron vacuum devices, such as magnetrons Does this look similar to diocotron?????

Micro Malmberg-Penning Trap Array Eliminates Problematic Axial Potentials

•  Minimal Axial Potential for Micro Trap –  V =~ 34 V to Fill One Micro Trap to 109 –  Voltage Constant to Fill to 5×1013

•  Large Trap V = 250 kV at 5 ×1013

L = 34 cm dp= 0.68 cm dw= 1.36 cm


•  Construct long aspect ratio trap for positron

•  Mechanical alignment with external magnetic field •  High vacuum with cooling of tube, hydrogen free

environment

•  Assemble several tubes to extend length •  Filling with positrons or particles •  Storage times, density, release

Proof of concept: engineering


“Shield and work together”: Natural “shielding”

Each tube: electric potentials reduce repulsion of particles

Metallic “mirror” between tubes: image potentials of conducting walls between parallel tubes shields particles from each other- ”Faraday Law” however note there are variations in the workfunctions that should average out variations?


“Let it be”: Many very long traps

Long trap and shielded : easy to confine axially, and radially shielded (metallic wall from each other Fermi School -

Varenna, July 2009

Reduce the interaction of the non-neutral plasma

One long endless metal tube chopped it into shorter segments and stack them in parallel within one magnetic field.

From one tube to Stack of segments of pipeline stores same amount


How many e+ to demonstrate?

Current Single trap

goal

~100 traps current style


Heating ( with no cooling included) plasma density (solid line, left scale) and confining end cap potentials (dashes, right scale) vs. trap radius. The density scales with the square of the magnetic field. Fermi School -

Varenna, July 2009

Surko density 109/cm3

Note this now just sums with the number of tube

Micro Trap Plasma Data •  Density

–  n+ = 2 × 1012 cm-3

–  nmax = 2 × 1013 cm-3

•  Cyclotron Cooling Rate: 645 ms

•  Plasma Interactions Weak to Moderate

–  After Filling: Tp is Large and Γ<<1

–  After Cooling: Tp≈ 4 K and Γ ≈ 8




Single crystal of Silicon (100) which has four fold symmetry to reduce and cancel path effects.

Other possibilities is to coat the inside walls with amorphous Material.

We will check the lifetime by Making each wafer so we can And changes the thickness of The wafer to simulated variations In the fields similar to patch effects.

Patch Effects- voltage variations

The start up of crossed-field amplifiers and magnetrons can result in noise detrimental to many applications. The transient of a 2d crossed field diode can be divided into three separate stages: cycloidal flow, collapse of cycloidal flow and non-uniform (E X B) sheared flow.

Recent 1d results show cycloidal flows will collapse into near Brillouin flow (P.J. Christenson, et. al. Phys. Plasmas), 3(12):4455-4462, Dec 1996.

In this study 2d electrostatic PIC simulations show that cycloidal flows also collapse into flow that is dominated by the E X B drift, but is not uniform or stable.

This observed instability has nothing to do with the magnetron or diocotron fluid instability (O. Buneman, et. al. JAP, 37(8):3203-22, July 1966).

After the perturbation from the collapse of the cycloidal flow saturates, eventually the fastest growing fluid instability will dominate the system.

Are there relationship of particle beams and plasmas??? Not much in the literature>>>

Micro Trap Plasma Data •  The cyclotron-cooling rate for electron mass

particles is approximately Γc = B2/4 where B is in tesla and Γc is in s -1

Cyclotron Cooling Rate: ~645 ms

•  Plasma Interactions Weak to Moderate

–  After Filling: Tp is Large and Γ<<1

–  After Cooling: Tp≈ 4 K and Γ ≈ 8 Fermi School - Varenna, July 2009

Scaling Up Micro MP Trapz Array •  Increase Number of Micro Traps

–  Increases Silicon and Magnet Diameter to 30 cm

–  ~1015 e+ / cm3 Requires 10 cm length with 6 cm diameter Magnet (1×107 Micro Traps with 108 e+)

•  Increase Number of e+ in Each Micro Trap where stability is maintained.

–  Closer to Brillouin Limit and will need to determine the lifetime to instabilities.

–  Increases Axial Potential (V = 340 V for 1010 in Each Micro Trap) -limit

•  Increase Magnetic Field

–  Brillouin Limit nmax ∝ B2 ( will run at few Telsa)

•  Increase Trap Length include cooling elements in sections if needed (Surko 2002)

•  Combination to Scale Up to Larger Quantities of e+ Fermi School - Varenna, July 2009

Multitrap Stack of “soda straws”

Insert trap in a cold bore superconducting magnet Of course in vacuum


Produced by John Bumgarner -SRI Fermi School - Varenna, July 2009

Note symmetry 30 microns

John Bumgarner -SRI Fermi School - Varenna, July 2009

Fermi School - Varenna, July 2009 Proof of Ion Traps

Vapor pressure H2

Need: Material with low H2 Low outgassing components Proven by cool traps


Vacuum requirements The annihilation rate for trapped positrons is expressed as ,

where ro is the classical electron radius, nn = density of neutral atoms in the trap. For atoms and small molecules the annihilation rate is on the order of the uncorrelated electron gas limit where Zeff≈Z. For large molecules and especially large hydrocarbons Zeff can be many orders of magnitude larger than Z. Annihilation lifetimes greater than 40 days will be achieved much below 10-10 Torr.


Malmberg et al 1988


In our design our B~ 5 T L~ 10 cm w/o RW

L/B = 2 x 10-4

tm = 106- 108 sec

Scaling-Technical Challenges •  Alignment of long tubes and magnetic field-

smaller diameter (< 100 µm)becomesmorechallenging

•  Homogeneous material -conditions at tube wall and end caps- variations in potentials -patch effects should average out

•  Vacuum pressure-cold wall traps low hydrogen should solve-Note recent CERN results

•  Quantum world: the particle wave packet overlaps with the tube walls –  de Broglie wavelength: λ = 6 nm @ 300 K Fermi School -

Varenna, July 2009

Roadmap •  Finish the new positron beam •  Implement field assisted moderation •  Determine if we need to use magnetic

funnel- works •  Build a single trap to prove the concept •  Build and test a small array of traps •  Scaling…to >1012 trapped positrons

small volume: Have trap, need positrons, will travel!

In progress


Source

Muffin tin electric field assisted moderator Trap tubes

Patterned beam profile Filling

Expanded view


Have modeled the fields

Ideas on pulse release


Release


Compacting Already stored positrons

New positrons

Block positrons from escape

Compact to make room for more


Release Trapped positron cloud for storage Confining

potentials and magnetic field

Compression

Gradual or sudden release for use: Annihilation photons Ions High energy density high and temperature

“Release”

Annihilation in target

“practice” with electrons


Fill / Release Trapped positron cloud for storage Confining

potentials and magnetic field

Compression

Gradual or sudden release for use: Annihilation photons Ions High energy density high and temperature

“Release”

Annihilation in target

“practice” with electrons


Squeeze: Time focusing;

bunching

Space focus


Penning trap micro-tube Fermi School - Varenna, July 2009

Quadratic buncher: single shot


Variable speed machine gun


Instant release

•  1012 positrons and electrons:

•  0.16 J pulse of 511 keV photons.

•  Time-averaged power is 8×108 W

1015 positrons


Heating

1015 positrons


Beyond proof of concept

•  Imagine: – Nano tube traps – 1015 carbon nano tubes with one positron

each or more – More tubes


What else to do with positrons? •  Materials defects, vacancies, voids 105-106

•  Thin film porosity 105-106 •  Quantum structures 105-106 •  Magnetic properties, at/near defects 106

•  Multiple photon annihilation 106-107

•  >1 antiparticle at a given time 108-109

–  Ps2 molecule, Ps-Atom or Ps-Ps molecule –  Many Ps system, BEC, equation of state

•  High energy density studies >>1010

•  Power source >>1015

Done at present


Proof of concept •  Build/use

–  Intense positron beam at WSU (Keck beam, 108/s) –  Micro-trap array with several 100 tubes –  Fill with 1012 positrons in small volume –  Characterize trap performance

•  WSU capabilities to micro manufacture multi-tube trap

•  Accelerator based positron source for filling •  Need superconducting magnet for tests •  Lots of science on the way


Single trap limitations •  Brillouin limit: Repulsive (and centrifugal) forces balanced by magnetic field:

ρ⋅mc2 < B2/(8π) –  High magnetic field (B) field is better

•  Space charge: Balance force against end cap potential: 1.4×10-7⋅ρ⋅V(1+2⋅ln(rt/rp))/Lp < Ucap

–  Longer trap (L) is better

•  Radial electric field: ExB effect causes radial drift:

Ucap < B2Lt2q/(4⋅mc2)

–  Higher magnetic field is better •  Vacuum: annihilation and scattering with residual gas: τ∝1/p = 1/(πcro

2nZeff) found 1/sqrt(p) dependence

•  Rotating wall confinement: squeezes particles together (we presently do not plan to implement)

Image from http://hyperphysics.phy-astr.gsu.edu/hbase/electric/vandeg.html Fermi School - Varenna, July 2009

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Dream for the Stars or at least way to store anti-matterstatic.sif.it/SIF/resources/public/files/va2009/lynn_0714a.pdf · Dream for the Stars or at least way to store anti-matter