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Laser Driven Plasma Collider for Nuclear Studies

Changbo Fu

Shanghai Jiaotong Univeristy Jun09, 2015

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Scientific Motivation 1

  “Full Plasma” Conditions for low nuclear studies?

•  Full Plasma is needed for Nucl. Astrophys. etc. •  Traditional Accelerator can not provide “Full Plasma”

From: Cauldron in cosmos, C. E. Rolfs

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Nuclear Parameters may be also diff in plasma or boundary

states.   7Be

•  7Beneutral t1/2 =52d( •  7Be4+ : Stable

  125Te 1st ex. st. (Z=52, E=35.5 keV)

•  Q=0 T1/2=1.5 ns (internal conversion + M1)

•  Q= 47+ T1/2 = 6 ± 1 ns F.Attalah et al., Phys.Rev.Lett. 75(1995) 1715

Why Full Plasma? ----Nucl. Parameters

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Scientific Motivation 2

  “Safe Nuclear Power” •  TOKMAK, Magnetic Confined Plasma •  ICF, Inertial Confined Fusion •  ADS, Accelerator Driven System

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The idea of “Laser Plasma Collider”

Collider

Accelerator Laser Driven Acc.

Laser Driven Collider

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“Laser Plasma Collider”

Laser Plasma Collider

Trad. Collider

Pulse Very narrow >ns Peak Density Very large Small

charge Neutral charged Repeat frq. Very low High

Cost Low High

Size Small Large

Beam Quality Bad good

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New Physics Under Extreme Conditions?

  Ultra-Narrow Pulse(e/p/gamma/n)   Ultra-high E-Field (1011V/m)   Ultra-high B-Field (102-105T)   Ultra-high pressure(1011 bar)   Ultra-high Temperature (105-1010K)

!  Very high Peak Current (100kA)

Laboratory Astrophysics

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1st prove-of-concept reaction D+D !n+3He+2.5MeV

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Expermental Setup

Normasky Interferometer

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2mm

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Target before and after shot

  a

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Neutron Spectra

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Stream 1 Stream 2 Overlap Region

4.4 mm

(a)

(c)

(b)

Jet 1 Jet 2

Overlap Region

3.5 mm

Jet 1 Jet 2

(d)

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Where did the products come from?

a

b

c

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Obtain Nuclear Reaction Cross Sections Experimentally

Cross Section Ion ρ/E

Yield E/PID/θ…

e ρ/E

Key is to Determine Ion’s ρ(x,y,z,t)

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Structure of Plasma ABC

 Driving Force •  EM (Large Scale) •  Gradient of Temperature •  Gradient of Density (Biermann Battery Effect) •  Scattering (EM, Nuclear Force, Maybe) •  Laser EM (1E15Hz)

is close to the square root of the proton energy ratio ofð15=3:3 MeVÞ1=2 # 2:1, strongly suggesting that the domi-nant source for proton deflections is magnetic fields ratherthan electric fields (15=3:3 MeV# 4:6). These fields musthave dominant azimuthal components (around the jet axis)and their strength is estimated by

ZB$ d‘ ¼ & AmpVp!

qðA& aÞa ; (1)

where a ¼ 1 cm and A ¼ 28 cm; mp is proton mass andVp is proton velocity; q is the proton electric charge, andd‘ is the differential pathlength along the proton trajectory.From Fig. 2, we obtain jRB$ d‘j# 15 T cm. Taking thescale size as the diameter of the flattened disk (from a 3Dconfiguration) ' 0:5 cm (slightly larger than the field ofview of our detector), results in a magnetic field roughly ofan order #30 T. Note that the magnetic deflection of thecarbon and hydrogen ions of the streams has an oppositesign on the two sides of the bisector plane. For fieldsweaker than #30 T a mutual neutralization of the deflec-tions may occur, restoring a simple conical ion flow in eachof the jets.

The head-on collisions were simulated with the two-dimensional (2D) hydrodynamic code [39,40]. Figure 3displays postprocessed snapshots showing the spatialstructure and temporal evolution of two counterstreamingplasma jets colliding with each other. The numerical simu-lation and Thomson scattering measurements [41] indicate

that the electron flow stagnates in the axis and subse-quently spreads sideways, forming a flattened region(a disk in 3D view) with typical ne # 1019–1020 cm&3

and Te # 500–1000 eV.To place the discussions in the broader context of basic

plasma physics, Table I gives physical parameters for thehead-on collisions. The long jet-jet ion mean-free pathindicates that the interjet ion-ion collisions are essentiallycollisionless. The general picture of the magnetic fieldbeing frozen into the electron fluid and advected alongits streamlines is only to be expected if the magneticReynolds number is high, and the estimated magneticReynolds number of Table I is gratifyingly large. Notethat the carbon gyroradius is comparable to or even smallerthan the size of the observed structures, indicating that theregular azimuthal field may cause the ions to be deflectedfrom their initial straight trajectories, create radial ion flowin both jets, significantly affecting the ion dynamics nearthe bisector plane. This happens despite the fact that themagnetic pressure pM of the 30 T field, as estimated fromthe measurements, is orders of magnitude smaller thanthe ram pressure "v2 of either of the jets: pM="v

2#2$ 10&3. The presence of the two counterpropagatingstreams makes this effect possible.The generation and advection of spontaneous magnetic

fields are described by the Faraday equation combinedwith a simplified version of the generalized Ohm’s law:@B=@t ¼ r$ ðu$BÞ þ S [9] whose azimuthal compo-nent B’ is given in the cylindrical coordinate as

@B’

@t¼ @

@rðB’urÞ &

@

@zðB’uzÞ þ S’; (2)

where ur (uz) is the radial (axial) component of the velocityof electron flow [1], and S’ is the source term for the fieldgeneration, which is dominated by the so-called Biermannbattery effect (rne $ rTe). The frozen-in condition forthe azimuthal field in axisymmetric effective flow is [1]

B’=ner ¼ const: (3)

This suggests that there exists a zone near the bisectorplane from which the plasma electron flow becomes almost

FIG. 3 (color online). 2D DRACO hydrodynamic simulations ofthe two head-on plasma jets which displays the jets’ formation att ) 1:4 ns; propagation at t ) 2:2 ns (a clear bow shock struc-ture is seen in front of the jets); the onset of plasma flow in thetransverse direction, and the formation of a high-pressure regionin the bisector plane, at t ) 2:6 ns; and the transverse expansionof the high-pressure region in the bisector plane t ) 4:1 ns. Inthis simulation, a low density (# 2$ 10&6 g cm&3) deuteriumgas has been added to the background. The simulation of plasmaflow (4.1 ns) appears to be quite consistent with the shape of theproton deflection images shown in Figs. 1 and 2.

TABLE I. Calculated parameters of two interpenetratingjets based on v ¼ 1:7$ 108 cm s&1, Te # 1 keV, nC # 4$1018 cm&3 (per jet), length scale of the overlap regionl# 0:3 cm, and strength of magnetic field #30 T.

Parameters

Carbon ion energy (WC) 175 keVCarbon ion gyroradius (rG) 0.8 mmJet-jet ion mean-free path (#ZZ) 20 cme-e collision frequency ($ee) 3$ 1010 s&1

Dynamic time (t ¼ l=v) 1:75$ 10&9 sMagnetic diffusivity (DM) 103 cm2 s&1

Magnetic Reynolds number (ReM) 5$ 104

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Structure of Plasma ABC

  Dynamic of Electrons and Ions •  m/q •  (Magnetic) Reynolds number •  Mean Free Path Collision Frequency) •  Gyroradius of electron ion

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radial, and the increasing plasma density due to contribu-tions from the other jet would lead to the increase ofmagnetic fields as this flow spreads sideways, which isconsistent with the observations (Fig. 1).

The streamlines of electron flow are modeled witha modification of an analytical description of head-oncollisions [1], where the flow follows a solution of thedifferential equation

dr

ur¼ dz

uZ(4)

in cylindrical coordinates, and the velocities ur and uz aregiven by Eqs. (21) and (22) of Ref. [1], respectively. Neareach target, the flow is diverging and the frozen-inBiermann battery field decreases along the streamlines.Shown in Fig. 4(c), the ‘‘conical’’ streamlines approachfrom both sides, stagnate, and subsequently spread side-ways, indicating the electron flow stagnates near the bisec-tor plane, and the magnetic field is recompressed to aquasiplanar structure [1,42]. The bisector plane acts as animpermeable boundary for electron fluid, and the recom-pressed field has an opposite handedness in the oppositeflows. By virtue of the frozen-in condition, the streamlinesdeviate toward much larger radii subsequent to the stagna-tion, leading to enhanced magnetic fields due to increasingproducts of density and radius [Eq. (3)]. These processesproduce a flattened structure along the bisector plane andmimic the observed Fig. 4(a) and simulated Fig. 4(b)structure.

To model the noncollinear collisions at an arbitraryangle, which are more generally relevant to those occurringin nature than collisions of perfectly collinear jets, aCartesian coordinate system is more convenient becausethe azimuthal symmetry is broken [Fig. 5(a)]. Normalizing

the distances to the parameter L (half distance between thetargets), an equation for the streamlines can be written as

arctan!1

!1arctan

y

x

"

þ f arctan!1

!2arctan

x sin2"þ y cos2"# 2 sin"

x cos2"# y sin2"# 2 cos"

"

¼ const; (5)

where f is the ratio of the flow strengths of the two jets and!1 and !2 are the angular half-widths of the flows withinthe two jets. For 90$ collisions where f ¼ 1, " ¼ 45$, andtaking !1 ¼ !2 % 0:2 radian (due to the jets being morecollimated in these experiments), one obtains the stream-line distribution shown in Fig. 5(b). The experimentalproton image is well simulated, with a narrow structurepointing in one direction and a much thicker one pointing inthe opposite direction in the bisector plane. This asymmetryis a consequence of collisions of tilted jets, which result information of stronger field compression (denser stream-lines) in the forward direction and weaker in the backwarddirection. Although collisionality may increase somewhatdue to a lower energy in the center-of-mass frame, the jets

FIG. 4 (color online). Proton image (a), numerical simulation(b), and analytical model (c) of streamlines of electron ‘‘effectiveflow’’ for collisions of two counterstreaming plasma jets (head-on).

2L α

αx

x′

y

y′

°

°

FIG. 5 (color online). Schematic drawing of coordinate system(a) to illustrate the collisions of two plasma jets at an angle ¼180$ # 2". Proton images of the collisions of two identicalplasma jets (white arrows) is compared with model predictedstreamlines of effective electron flow at 90$ (" ¼ 45$) in (b) and135$ (" ¼ 22:5$) in (c), respectively. The dashed-dotted linesshown in the images indicate the bisector planes.

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  Electron (NOT Ion) obtains high energy from Laser field

  Electrons fly away Drag the Ions together

  e-e e-i; i-i scattering   E field   M field strength   Reynolds Number >20

Our neutron Yields consistent with the prediction

PRL.111(2013)235003

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2nd exp: D+ 6,7Li Driven by Laser

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6Li/7Li Abundance Problem

,

He 0.248D/p 2.64E-53He/p 1.06E-5 (0.9—1.3)E-57Li/p 4.22E-106Li/p 1E-5

2.78−0.38+0.44 ×10−5

0.249± 0.009

1.23−0.32+0.68 ×10−10

1×10−2

Journal of Physics: Conference Series 202 (2010) 012001 doi:10.1088/1742-6596/202/1/012001

The Big Bang Mode can predict the abundence of p/D/He4 very well. However, the 7Li�6Li abundance have serious problem!

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  Three body reaction?   D+7Li!g.s. (0+)

!1st e.s.(2+) !2nd e.s.(4+)

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D+Li Preliminary Results

Preliminary

g.s

1st ex.

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D+Li Preliminary Results

Preliminary

g.s

2nd ex.

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Future Improvement

  Understanding the Hydrodynamic of the Plasma is the KEY for “plasma collider” app.   Different Diagnostic Methods should be developed

•  TOF •  Tomography

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Summary

  We carried out, for the 1st time, “Laser Plasma Collider” for low energy nucl. phys. studies.

  We studied D+D reactions, and proved that Most of the reaction products coming from plasma collision.

  Promisingly, the method could be used for D+Li7, the reaction to solve the Li7 abundance puzzle for the Big Bang theory.

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Collaborators

  Changbo Fu, Yang Sun, Liang Li, Xiaopeng Zhang, Ji Zhang (Shanghai JiaoTong U.) Yutong Li, Liming Chen, Jiarui Zhao, Baojun Zhu, Guoqian Liao, Yanfei Li (Inst. Phy., CAS) Jianjun He, Shiwei Xu(Inst. of Mod. Phys. CAS) Jie Bao, Long Hou(China Inst. of Atomic Eng.)   Yongjoo Rhee (Nucl. Data Center, Korea)   Dawei Yuan, Gang Zhao (Nat.Astro. Obs. CAS)   Jianqiang Zhu(SH Inst. Op.& Fine Mech., CAS)