03pC01
ナノチューブ加速器によるプロトン加速	 
Proton Beams from Nanotube Accelerator
村上匡且1、田中基彦2Masakatsu MURAKMI1, Motohiko TANAKA2
阪大レーザー研1、中部大工学部2
ILE Osaka Univ.1, Chubu Univ.2
1. Introduction
Ion acceleration driven by ultraintense ultrashortlaser pulses has been intensively studied in the past
decade because a number of future applications areexpected. For practical use of the accelerated ions, it is
crucial to produce high-quality beams that aremonoenergetic and collimated. We here propose anovel ion acceleration scheme using carbon nanotubes(CNTs) [1], in which embedded fragments of low-Zmaterials are irradiated by an ultrashort intense laser toeject substantial numbers of electrons [2, 3]. Due to theresultant unique electrostatic field, the nanotube andembedded materials play the roles of the barrel andbullets of a gun, respectively, to produce highly
collimated and quasimonoenergetic ion beams.
2. The nanotube accelerator
Figure 1 shows the schematic view of a nanotube
accelerator. The double nested nanotubes are irradiatedby an ultrashort intense laser pulse. The outer carbon
nanotube is chemically adsorbed with heavy atoms
such as gold, while the inner nanotube is made of lightmaterials such as hydrogen and carbon to form theprojectiles. Upon laser irradiation, electrons inside thenanotubes are ejected within a few laser cycles(comprising the small white particles around thenanotubes). The remaining nanotubes composed of
positive ions generate a unique electrostatic Coulomb
field so that the inner ions are accelerated along theaxis symmetrically toward both ends of the outer
nanotube. As a result, a pair of quasimonoenergetic
collimated ion beams are obtained.
3. N-body simulation
We have performed N-body charged particle
simulations, in which all of the particle-to-particle
Coulomb forces are computed exactly. The relativistic
version of the Newtonian equations of motion are used,similar to molecular dynamics simulations of
microwave heating of salty water and ice. Moreover,
our simulation includes the Lennard-Jones attractive
potentials for pairs of like atoms, and repulsive
potentials for other species as a core exclusion to avoid

Fig.1 Schematic view of a nanotube accelerator. Upon laserirradiation, electrons inside the nanotubes are ejected within a few
laser cycles. The remaining nanotubes composed of positive ionsgenerate a characteristic electrostatic Coulomb field so that theinner ions are accelerated along the axis symmetrically toward bothends of the outer nanotube.

numerical divergences. Such N-body simulations are
the most suitable numerical approach for treating
parametric domains in which the plasma scale becomessignificantly shorter than the Debye length.
Figure 2 shows snapshots of the nanotube
accelerator dynamics at sequential times, obtained inthe N-body simulations in a side view (upper row) andtop view (lower row). The outer nanotube is of 30 nm
in length and 15 nm in diameter, with gold atoms(yellow) chemically adsorbed onto the carbon atoms(green). Inside the nanotube, two cylindrical bullet
nanotubes made of hydrogen (red) are embedded.
Sinusoidal laser light is applied with intensity IL = 1018
W cm-2. During the first laser cycle, ionized electrons(white) are ejected by the laser field. Simultaneously
the saddle-shaped Coulomb field forms to squeeze andaccelerate the projectile ions along the z-axis.
At t = 0, sinusoidal laser light is incident on thenanotube from a radial direction normal to the axis.
The linearly polarized electric field is EL=E0 sin(2πT )15nm

EL
EL

T = 0.5

4dN rdE

12T = 1.5Fig.%3

for T > 0, where T = t/t0 is the time normalized to thelaser period t0 = 2.7 fs for a titanium-sapphire laser at awavelength of lL = 0.8μm.
In Fig. 2, the field amplitude is E0 = 3 x 1012 V m-1,corresponding to a laser intensity of IL = 1018 W cm-2.
At such an intensity, the gold atoms are photoionized
to a state of about ZAu = 20, while the carbon andhydrogen atoms are fully ionized to ZC = 6 and ZH = 1,respectively. If the laser is irradiated from one side, thepresent scheme has an applicable upper limit (IL ~ 1020W cm-2) to keep high collimation performance, overwhich the ions are also accelerated by ponderamotive
force along the same direction of the incident laser.
The maximum ion energy is expected to increase withthe system size and laser intensity according to theprinciples of a Coulomb explosion [4, 5].
4. Energy spectrum
Figure 3 shows temporal evolution of the protonenergy spectrum in the axial (solid curves) and radial(dashed curve at T = 5) directions. Corresponding
two-dimensional dynamics has been shown in Fig. 2.
Quasimonoenergetic protons with an energy of Emax =1.5 MeV are produced at T = 5. If the hydrogen atoms
are replaced by carbon atoms, the maximum ion
energy increases to 10 MeV for the same target
structure. The maximum energy can also be increased
by enlarging the target size.
A good measure of the collimation is Ez/Er, whereEz and Er denote the average kinetic energies of theprojectile ions in the axial and radial directions,respectively. In Fig. 3, Ez ~ 1.4 MeV and Er ~ 0.017
MeV for the final stage of acceleration at T = 5, so that
Ez/Er ~ 85, which indicates a strikingly high degree ofcollimation. Finally, the energy coupling efficiency hc
is an important index of the ion beam generation froman engineering point of view. It is defined as the ratioof the integrated kinetic energy of the projectile ions tothe absorbed laser energy. In the present work, thevalues of hc are of the order of 1% or less. BydNzdE

54T=58

T=43642

T=31200

T = 2.0

Fig.2 Temporal evolution of Nanotube Accelerator

T=5100

T = 1.0

x10
60.5

11.54zx10
14

Axial energy spectrum dN /dEr

Radial energy spectrum dN /dE

Top%view%%%%%%%%%%%%%%%%%%Side%view

15nm

2Proton kinetic energy E (MeV)
Fig.3 Temporal evolution of proton energy spectrum

optimizing the design of the nanotube structure andlaser parameters, hc is expected to increase to severalpercent.
5. Summary
We have proposed an ion acceleration scheme using
structured nanotubes, that operate under irradiance ofultrashort ultraintense laser pulses, to produce
high-quality ion beams. Detailed three-dimensional
particle simulation has demonstrated the generation ofquasimonoenergetic highly-collimated 1.5-MeV proton
beams. The present concept leads to a view of CNTs
different from an existing one, that until now had only
been considered to be solid-state devices. It has been
demonstrated that spatial control in nanoscale
fabrication is as crucial as temporal control in femtoscale laser operation. For further practical studies ofthe present scheme, it will be crucial that multiple
nanotubes are uniformly produced in size anduniformly arranged in direction.
References[1] S. Iijima, Nature 354, 56 (1991).
[2] M. Murakami and M. Tanaka, Appl. Phys. Lett. 102,163101 (2013).
[3] S.G. Benka, Physics Today 66 (June), p.17 (2013).
[4] M. Murakami and K. Mima, Phys. Plasmas 16,103108 (2009).
[5] B. Ramakrishna, M. Murakami, M. Borghesi et al.,Phys. Plasmas 17, 083113 (2010).