1、Electron acceleration in wake bubble by ultraintense laser interacting with plasma,Bai-Song Xie and Hai-Cheng WuCollege of Nuclear Science and Technology,Beijing Normal University, Beijing 100875Peoples Republic of China19, Aug. 2010,Outline,Modification of bubble core field by bubble interior resid
2、ue electrons (空泡内部残余电子对空泡内部场的修正）Optimizing electrons acceleration of wake bubble with dense-plasma wall (利用高密度等离子体壁优化空泡加速中的电子加速),Laser-Plasma Wakefield Acceleration,T. Tajima and J. M. Dawson, PRL 43, 267 (1979),Thomas and Katsouleas, Nature 431, 515 (2004).,Electrons acceleration in bubble,Electron
3、s void, higher acceleration field gradientBubble is robustWave-breaking and self-injection occurs at bubble bottom Linear scaling law of bubble core fieldMonoenergetic energy,A. Pukhov and J. Meyer-Ter-Vehn, Appl. Phys. B 74, 355 (2002).,Linear scaling laws of bubble core fields,I. Kostyukov et al.
4、Phys. of Plasmas 11, 5256 (2004).,6,Outlook,Modification of bubble core field by bubble interior residue electrons Optimizing electrons acceleration of wake bubble with dense-plasma wall,Electrons density and velocity,Plasma density,Laser parameters,A: modification of bubble core fields based on Kos
5、tyukov model,I. Kostyukov et al. Phys. of Plasmas 11, 5256 (2004).,Quasistatic approximation when ignoring,In bubble core region,Slope of longitudinal field 1/2, slope of transverse are reduced.,3D cylindrical case,2D planar case,Approximately the bubble shape is given by the potential surface. Rati
6、o of longitudinal to transverse radius,Comparison by modification theory with PIC simulation results,Comparison by modification theory with PIC simulation results,Electrons charge and current density:Equi-potential surface: Moving frame:,B: modification of bubble core fields based on elliptic bubble
7、 shape,In the condition of Lorenz gauge,Back transformation to laboratory frame,Similarly in 2D case,Quasistatic approximation, bubble velocity c, Lorenz gaugeW. Lu et al. Phys. Plasmas 13, 056709 (2006).,C: modification of bubble core fields based on Lu model,Electromagnetic fields solution:,Bounda
8、ry conditions:( r = ) = 0:,Electrons motion equation of bubble wall,When rb1, and in bubble region of no laser pulse, no driving source and no self-injection e-bunchComparison with elliptic equationFields slope near to bubble core,Brief summary,Electron that enter the bubble moves backward with c, w
9、hich weaken the transverse fields, leads to reduction of ratio of longitudinal to transverse radius of bubble shape.Smaller ratio compensates the weakness of longitudinal field due to entered electrons so that the longitudinal field is hardly changed.The slope of transverse fields are reduced almost
10、 2 times. This makes a possible to increase the accelerated e-bunch transverse emittance.For same transverse size bubble, because the longitudinally shrink, the corresponding de-phasing length is also shrunk that is disadvantage to get higher e-energy.,24,Outline,Modification of bubble core field by
11、 bubble interior residue electrons Optimizing electrons acceleration of wake bubble with dense-plasma wall,Introduction,Two key points: electrons injection and acceleration optimizationLack of efficient schemeRayleigh diffraction length, laser pulse depletion length, electrons acceleration de-phasin
12、g lengthDecreasing plasma density or/and enlarge the bubble size Enlongating the laser pulse depletion length as well electrons acceleration de-phasing lengthContinuous self-injection influnces energy peak and energy spreadTwo open problems: increasing of electrons acceleration de-phasing length and
13、 suppression of electrons continuous self-injection,Simulation parameters,laser,plasma,I mm length homogenous underdense plasma with vacuum and preplasma in left,dense plasma wall,Wall density,Wall thickness,Wall inner radius is a little larger than the initial bubble transverse size,ZLP-laser, plas
14、ma with no dense-plasma wall,(a) self-focus:(b) move a ZR again, back overtake fore, guiding loss, diffraction at two lateral side, e-bunch length 48, 1010 number.(c) move a 1.2 ZR again, e- bunch length 40, 1010 number. (some electrons overtake the centre so that e-bunch length is shorten)(d) large
15、 e-bunch spatial divergence, multi-peak energy spectrum, wide energy spreading.,(a): a 24, = 0, Est. 8.24, PIC 9.1(b): a 32, = 2.18, Est. 14.8, PIC 15.4,Estimation of bubble transverse size,ZLP-laser with dense-plasma wall Rw=11.31,(i) continuous self-injection; (ii) e-bunch tailoring; (iii) quasi s
16、table phase accelerationAs bubble grows it touches the dense-plasma wall, results in a thin layer high-density ions in the bubble transverse lateral side due to the wall layer electrons slightly move away wall. The high-density electrons near the wall screen quickly the fields of bubble that constit
17、ute a new wall and prevent the bubble further growthhigh-density positive charge layer enhances longitudinal field, half e-sheath at back is shorten and e-bunch is tailoredThe tailored e-bunch pushes the electrons at its front and drives out a 2nd bubble. It enhances the electrons density at bottom
18、of 1st bubble and enforces furthermore longitudinal field,ZLP-laser with dense-plasma wall,During 1ps - 2ps, the accelerated e numbers is less and less and almost unchanged after 2ps. The bubble bottom shorten and e-bunch tailored processes slows down until end.The bubble shrunk longitudinally slows
19、 down: (i) under a dense-plasma wall radius, the bubble size should be determined finally by consistent balance conditions; (ii) The accelerated e-bunch is shorten that make the transverse repulsion reduced; (iii) The tailored e-bunch is depleted continuously that leads its ability to push bottom el
20、ectrons and enhancing longitudinal field becomes weaker and weaker,The tailored e-bunch pushes the electrons and enforces longitudinal fieldSome bottom electros follows the accelerated e-bunch to move forwardly. At t=3.5ps, e momentum 103mc. The accelerated e-bunch is always at botom so that it can
21、be almost stable phase accelerated.Bubble longitudinally shrunk, high-density positive charge thin layer presence and high-density electrons of bottom enhance the longitudinal field, e.g. at t=2ps, the slope of longitudinal field 1.7 0.5High acceleration gradient +stable phase high energy, narrow en
22、ergy spread, high collimation.energy peak 2GeV, energy spread 4%, divergence angle 25mrad.,CP-laser,Asymmetric transversely bubble shape is due to the phase of laser pulse envelop,Rw=12.25ay=az=20/sqrt(2)Peak energy 2GeV Energy spread 10%Electrons number 109/2,YLP-laser,Rw=12.25ay=20Peak energy 1.2G
23、eV Energy spread 4.4%Electrons number 109/2,Brief summary,A dense-plasma wall with radius about as between bubble initial and largest transverse sizes.The shrunk bubble tailors part self-injected e-bunch and suppresses further self-injection. It can increase the monoenergetic e-bunch production.Acce
24、lerated electrons stay almost at the bottom of bubble not only increase the average acceleration field gradient but also overcome the limit of electrons acceleration de-phasing length to some extent.Three key factors: longitudinal shrink, dense positive-charge thin layer, and very dense electrons at
25、 bottom of bubble.,Summary,Analyzing theoretically the effect of electrons charge and current densities on the bubble core fields and bubble shape due to entering of electrons from bubble front into bubble core. Proposing an optimizing scheme by placing a dense-plasma wall with radius comparable to bubble transverse size that can suppress the electrons continuous self-injection and therefore it can increase acceleration gradient through a realization of quasi-stable phase.,Thanks,
