S8-5
kT-class Magnetic Fields in Laser Fusion Research
レーザー核融合研究における強磁場Tomoyuki Johzaki
城﨑知至
Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan
広島大学 大学院工学研究院 〒739-8527 東広島市鏡山1-4-1

In fast ignition laser fusion, application of kT-class longitudinal magnetic fields to fast electron beam
guiding is proposed for enhancing the core heating efficiency. From the collisional PIC simulations,
we demonstrated the sufficient beam guiding performance by kT-class external magnetic fields. Theeffect of the magnetic mirror configuration formed via fuel shell implosion was also discussed. Thebeam guiding and focusing is expected for the case with the moderate mirror ratio (RM~10). For thehigher mirror ratio (RM > 20), the refection due to mirror configuration exceeds the guiding effects,
which will reduce the heating efficiency.

1. Introduction
One of the most crucial issues of fast ignition[1] is efficient core heating by laser produced fastelectron beam. The main factors in preventing
efficient heating are (1) too high fast electronenergy and (2) too large beam divergence. The
fast electron energy could be controlled byeliminating pre-plasma generation and by using
heating laser with shorter wavelength. As for thebeam divergence, some ideas of the guiding of
the fast electron beam with large beam
divergence have been proposed, e.g., the double
cone [2-4] and the resistive guiding [5-10], where
the self-generated magnetic fields are used. The
guiding concept using the externally applied
longitudinal magnetic fields has been also
proposed [11,12]. In the present paper, on thebasis of the numerical simulations, wedemonstrate the effects of external magnetic
fields on the fast electron generation andtransport in the fast ignition condition.
2. Simulation Setup
If the sufficiently strong magnetic fields areapplied, the fast electrons are trapped by themagnetic fields and move along the magnetic fieldlines, and then the beam guiding by longitudinalmagnetic fields can be expected. The 2D
collisionless PIC simulations [13] showed thatseveral kT fields are required for beam guiding. In
the simulations, however, the longitudinal magnetic
fields were uniformly applied and the pulse
duration was only 100fs. For more practical study,in the present paper, we carried out the collisional
PIC simulations using relativistic electro-magnetic
particle in cell code PICLS [14] by assuming theconverging fields and longer pulse duration. Thetarget is initially fully ionized carbon foil (30 mwidth, 25 m thickness), and the electron numberdensity ne is 300 ncr (ncr is the laser critical density).
The pre-plasma with the exponential profile (3 mscale length) is attached on the target front surface.
The p-polarized laser pulse with wavelengthof L =1 m and the intensity of IL = 3x1019 W/cm2 isnormally irradiated on the target surface. The
transverse intensity profile is the Gaussian with aspot size of 6 m FWHM, and the temporal profileis 1 ps flat pulse.
3. Beam Guiding under Converging Fields
In fast ignition experiments, the magnetic fields
applied to the target are compressed by the fuelimplosion, so that the field structure becomes aconverging mirror one; the fields are weak aroundthe fast electron generation region, and then it isintensified toward the dense core region. In such a
converging structure, in addition to the guiding
effects, we should concern about the reflection of
fast electrons due to mirror fields. To evaluate theguiding effects under the converging fields, we
carried out the simulations by assuming theconverging fields with the mirror ratio RM =1~20 as
the initial magnetic field structure in PIC
simulations,Figure 1 shows the spatial profile of fast electronenergy density and magnetic field structure
obtained for the case with RM = 5. Though part of
the fast electrons are scattered or reflected due tothe mirror fields, the beam can be collimatedaround the beam axis along the magnetic field lines.
In addition, it is found in Fig.1(c) that thelongitudinal magnetic field (Bx) around the beam

axis observed at x = 37 m, which is initially ~10kT, becomes weaker (less than 5 kT). On the otherhand, it is intensified around the beam edge (higherthan 10 kT). In addition, the magnetic fields inz-direction are generated around the beam edge in adirection to confine the electron beam. So, the“magnetic pipe” [13] like structure is formed. Thesemagnetic field evolution is basically due to theresistive effects since these structure cannot beobserved in the collisionless simulations.
We evaluated the guiding effects by observing
the fast electron beam energy within 4 m width at
x = 37m, where the applied magnetic field
becomes maximum. In Fig.2, the energy conversion
efficiency from laser to the observed fast electronsLob2 is plotted as a function of RM. For theparallel field case (RM=1), Lob2 becomes twice
larger than that for the case without external
magnetic field. For the moderate converging fieldcase (RM=5), further enhancement is observed,
Lob2 nearly tripled. However, in further highmirror ratio region (RM > 5), the conversion
efficiency decreases with increasing RM. For RM =20, the mirror refection effect is comparable to theguiding effect. Further enhancement of RM will
reduce the conversion efficiency Lob2 from thevalue for the case without external fields. Theseresults indicate that the optimization of field
configuration for the beam guiding is required. The
acceptable mirror ratio of guiding fields is less than
20. Such field structure might be formed by controlof applying timing of the external field to the fuelshell, and of the configuration of a fuel shell and afiled generation coil.

Fig.1. Spatial profiles at 990 fs for case with RM = 5. Two
dimensional profiles of (a) fast electron energy density enormalized by mec2ncr, me and c are the electron rest massand the speed of light and (b) (Bx2+ By2)1/2 [100MG] andperpendicular profiles of (c) Bx, (d) Bz and (e) normalized
e observed at x = 37m.

Fig.2. Energy conversion efficiency from laser to fastelectrons observed within 4 m width at x = 37 m(maximum field region) as a function of mirror ratio.

4. Concluding Remarks
In one instance of kT-class magnetic field
application in laser fusion, the fast electron beam
guiding in fast ignition was referred in the present
paper. Further investigation is needed such as laser
intensity dependence, pulse duration dependence andformation of the optimal field structure. Also, theexperimental demonstration is indispensable.
Acknowledgments
This work is partially conducted under the joint
research projects of the ILE, Osaka University(FIREX-project), and with the supports of the NIFS
Collaboration
Researchprogram(NIFS12KUGK057 and NIFS14KNSS054) andJSPS KAKENHI Grant Number 25400534.
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