798
C. Joshi et al.
electrons and ions in such a wave with wavelength λ p = 2πc/ω p —as
E o ≈
m e cω p
e ,
E o (eV/m) ≈ 96.2
n o
cm −3
.
(12.1)
Here λ p is the plasma wavelength, ω p =
4πe 2 n o /m e is the plasma frequency
and n o is the background plasma density, c is the speed of light, m e and e are the
mass and charge of an electron, respectively. The majority of plasma accelerators
have been operated at plasma densities 10 14 cm −3 < n o < 10 20 cm −3 giving
10 9 < E o (eV/m) < 10 12 . Such ultrahigh accelerating gradients are the principal
attraction of plasma accelerators.
In a laser-plasma accelerator (LPA), an accelerating structure is created as an
intense laser pulse propagates through the plasma driving an electron plasma wave
also known as a wake. Specifically it is the ponderomotive force, F p , of the intense
laser that displaces the electrons from the heavier ions creating the charge separation
and accelerating wakefield. The ponderomotive force is related to E l or A l , the
electric field and vector potential of the laser respectively via F p ∝ ∇E 2
l ∝ ∇A 2
l .
Often the normalized vector potential of the laser driver, a o , is used to characterize
the strength or magnitude of the laser driver and subsequent wake that is driven. The
normalized vector potential of the laser is given by
a o =
eA l
m e c 2 =
eE l
ω o m e c
8.6 × 10
−10 λ o (μm)
I o
W/cm 2
,
(12.2)
where I o is the focused intensity of the laser pulse, and λ o and ω o are the vacuum
laser wavelength and frequency respectively. In laser wakefield accelerators, laser
intensities of 10 17 < I o (W/cm 2 ) < 10 20 are commonly used. For a o ≈ 1 and laser
pulse duration on the order of half-a-plasma wavelength (typically 50–100 fs),
wakes with accelerating fields of approximately 100 GeV/m are produced in a
10 18 /cm 3 density plasma. This gradient is more than three orders of magnitude
larger than the accelerating gradient in a conventional RF driven accelerator.
It was recognized in the 1980s that wakes in plasmas could also be driven by a
relativistic beam of electrons [2]. Given an intense enough beam of electrons, the
plasma is both created [3] and excited by the passage of the bunch. Recently, driving
the wake with a proton bunch has also been suggested [4].
In a beam-driven plasma wakefield accelerator (PWA), it is the space charge
force of a highly relativistic beam of particles which excites the wakefield. For such
a bunch, the electric field seen by the plasma electrons is in the transverse direction,
and the plasma electrons initially move away from the beam axis, while the more
massive ions remain effectively frozen. These transversely expelled electrons are
attracted back towards the beam axis by the space charge force of the ions, creating
a cavity with very strong electric fields. An appropriately timed witness bunch can
be placed in a region of very strong longitudinal component of the electric field of
this cavity and accelerated. See Fig. 12.1. The cavity also provides a radial force that
C. Joshi et al.
electrons and ions in such a wave with wavelength λ p = 2πc/ω p —as
E o ≈
m e cω p
e ,
E o (eV/m) ≈ 96.2
n o
cm −3
.
(12.1)
Here λ p is the plasma wavelength, ω p =
4πe 2 n o /m e is the plasma frequency
and n o is the background plasma density, c is the speed of light, m e and e are the
mass and charge of an electron, respectively. The majority of plasma accelerators
have been operated at plasma densities 10 14 cm −3 < n o < 10 20 cm −3 giving
10 9 < E o (eV/m) < 10 12 . Such ultrahigh accelerating gradients are the principal
attraction of plasma accelerators.
In a laser-plasma accelerator (LPA), an accelerating structure is created as an
intense laser pulse propagates through the plasma driving an electron plasma wave
also known as a wake. Specifically it is the ponderomotive force, F p , of the intense
laser that displaces the electrons from the heavier ions creating the charge separation
and accelerating wakefield. The ponderomotive force is related to E l or A l , the
electric field and vector potential of the laser respectively via F p ∝ ∇E 2
l ∝ ∇A 2
l .
Often the normalized vector potential of the laser driver, a o , is used to characterize
the strength or magnitude of the laser driver and subsequent wake that is driven. The
normalized vector potential of the laser is given by
a o =
eA l
m e c 2 =
eE l
ω o m e c
8.6 × 10
−10 λ o (μm)
I o
W/cm 2
,
(12.2)
where I o is the focused intensity of the laser pulse, and λ o and ω o are the vacuum
laser wavelength and frequency respectively. In laser wakefield accelerators, laser
intensities of 10 17 < I o (W/cm 2 ) < 10 20 are commonly used. For a o ≈ 1 and laser
pulse duration on the order of half-a-plasma wavelength (typically 50–100 fs),
wakes with accelerating fields of approximately 100 GeV/m are produced in a
10 18 /cm 3 density plasma. This gradient is more than three orders of magnitude
larger than the accelerating gradient in a conventional RF driven accelerator.
It was recognized in the 1980s that wakes in plasmas could also be driven by a
relativistic beam of electrons [2]. Given an intense enough beam of electrons, the
plasma is both created [3] and excited by the passage of the bunch. Recently, driving
the wake with a proton bunch has also been suggested [4].
In a beam-driven plasma wakefield accelerator (PWA), it is the space charge
force of a highly relativistic beam of particles which excites the wakefield. For such
a bunch, the electric field seen by the plasma electrons is in the transverse direction,
and the plasma electrons initially move away from the beam axis, while the more
massive ions remain effectively frozen. These transversely expelled electrons are
attracted back towards the beam axis by the space charge force of the ions, creating
a cavity with very strong electric fields. An appropriately timed witness bunch can
be placed in a region of very strong longitudinal component of the electric field of
this cavity and accelerated. See Fig. 12.1. The cavity also provides a radial force that