Omega Volume VII-System Description User manual

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1.0 Introduction ................................................................................................. 1
1.1 Scientic Mission ...................................................................................... 1
1.1.1 High-Power, High-Energy, and Proton-Beam Radiography.......... 3
1.1.2 HED Backlighting Experiments .................................................... 4
1.1.2.1 Cryogenic Implosion Fuel Conditions............................. 4
1.1.2.2 High-Temperature Opacity Measurements...................... 5
1.1.3 Fast Ignition ................................................................................... 5
1.1.3.1 Background..................................................................... 5
1.1.3.2 OMEGA EP Fast-Ignition Program ............................... 6
1.1.3.2.1 Intensity Scaling of Hot-Electron Energy ...................... 6
1.1.3.2.2 Electron-Beam Transport................................................ 6
1.1.4 SSP-Related High-Energy-Density Physics................................... 6
1.1.4.1 Equation of State Measurements of Materials................ 7
1.1.4.2 Isentropic Compression.................................................. 8
1.1.4.3 Isochoric Heating Experiments ...................................... 8
1.1.4.4 Hydrodynamic Instability Experiments.......................... 8
1.1.4.5 Indirect-Drive Experiments ............................................ 9
1.2 S C............................................................................. 9
1.3 S P S...................................................... 12
1.3.1 Short-Pulse Performance ............................................................... 12
1.3.2 Long-Pulse Performance................................................................ 13
OMEGA EP
System Operations Manual
Volume VII–System Description
Chapter 1: System Overview

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1.4 L S S........................................................................ 14
1.4.1 Laser Sources 1 and 2 .................................................................... 14
1.4.2 Laser Sources 3 and 4 .................................................................... 16
1.5 L B C ............................................................. 16
1.5.1 Beam Transport.............................................................................. 18
1.5.2 Grating Compressor Chamber ....................................................... 20
1.5.3 Target Chamber and Target Area Structure.................................... 23
1.6 T S .......................................................................................... 24
1.7 O A................................................................................... 26
1.8 L D..................................................................................... 29
1.8.1 Infrared Diagnostic Package (IRDP) ............................................. 29
1.8.2 Short-Pulse Diagnostics Package (SPDP) ..................................... 29
1.8.3 Ultraviolet Diagnostic Package (UVDP)....................................... 30
1.8.4 Full-Aperture Calorimetry ............................................................ 30
1.9 C S  J O P....................................... 31
1.9.1 OMEGA EP Control Room ........................................................... 32
1.9.2 Shot Types and Closed Access....................................................... 33
1.9.3 Shot Request Forms....................................................................... 35
A A: G  A

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Chapter 1
System Overview
1.0 I
This chapter provides an overview of the OMEGA EP Laser System. The scientic mission of the
laser is described in Sec. 1.1. Section 1.2 provides an overview of the system conguration, and Sec. 1.3
provides a summary of the system specications and laser energy requirements to meet the scientic
mission. Sections 1.4 and 1.5 describe the laser-sources and beamline conguration, including the grating
compressor and target chambers. Sections 1.6 and 1.7 describe the timing and optical alignment of the
system. Section 1.8 describes the laser diagnostics used to characterize the beams and Sec. 1.9 describes
the control system and the operations plan.
1.1 S M
The primary experimental congurations possible using the four OMEGA EP beams are
summarized in Table 1.1. Two short-pulse beams can be co-propagated to either the OMEGA or
OMEGA EP target chambers for backlighting or fast-ignition experiments. Alternatively on OMEGA
EP, the short pulse beams can be propagated orthogonally for backlighting and sidelighting. Compressed
pulses from the upper of two pulse compressors may be propagated at full energy (2.6 kJ) with pulse
widths as short as 10 ps. B-integral constraints limit the pulse-width/pulse-energy trade-off of the pulse
emerging from the lower pulse compressor except when used for sidelighting applications in the OMEGA
EP target chamber. Alternatively, all four beams may be directed into the OMEGA EP chamber, with each
beam capable of being operated in long-pulse (UV) mode with independent temporal-pulse shapes and
pulse widths up to 10 ns. It is also possible to send two compressed pulses and two frequency-converted
pulses into the OMEGA EP target chamber on the same shot.
Five primary applications of the OMEGA EP laser beams that take advantage of this exibility
are summarized below. Two applications of the OMEGA EP beams to the current OMEGA Facility
are described rst, followed by three classes of experiments to be carried out in the OMEGA EP target
chamber. When all 60 beams of OMEGA are used to generate a symmetric implosion, the only way to
provide backlighting is to add additional beams to the system. The short-pulse, high-energy beams of
OMEGA EP are capable of backlighting implosions with sufcient brightness to overcome target self-
emission and are of a short enough duration to overcome motional blurring.
(a) Short-pulse backlighting in the existing OMEGA target chamber
One or both of the compressed beams can be used to backlight targets in the OMEGA target
chamber with pulse-durations from 1 to 100 ps. As described in more detail in Sec. 1.1.1, high-intensity,
short-pulse lasers generate signicant uxes of high-energy x rays (>15 keV to ~1 MeV) and energetic
protons. Using the compressed beams as backlighters signicantly enhances the options available and
allows a wider range of high-energy-density (HED) physics experiments to be performed on OMEGA
than previously possible. High-brightness backlighting sources with greatly improved temporal resolution
allow spherical inertial connement fusion (ICF) implosions to be backlit. The two high-energy petawatt

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beams copropagate into the OMEGA target chamber but can be pointed and focused to different locations
within ~1 mm.
(b) Fast-ignition studies in the existing 60-beam OMEGA target chamber
The two compressed beams will be transported to the existing OMEGA target chamber as coaxial
beams with a common focus. The rst beam will be used to make a channel in the plasma atmosphere
surrounding the target through which the second (~5- to ~20-ps ignitor) beam, will propagate to the
high-density region in the target before depositing its energy, via energetic electrons, in the compressed
core, heating the plasma and increasing the fusion yield. Using the OMEGA EP beams, LLE will be
uniquely able to study aspects of the fast-ignition approach to ICF because of the high areal densities
and high electrical conductivity of compressed DT available with OMEGA’s cryogenic capability.
Recent work has shown that the fast-electron beam integrity in high-intensity laser–target interactions
of the target improves with increased electrical conductivity. No experiment to date has a target with
conductivity within an order of magnitude of that of a DT plasma. Fast ignition could increase the
utility of compression facilities for inertial fusion energy (IFE) research. Research activities will be
Table 1.1: Possible congurations for the four OMEGA EP beams in compressed
(short) pulse or long-pulse applications. Pulse-width limitations result
from design choices or by the B-integral of the beam combiner optic at
the end of the pulse compressor.
Co-propagating beams
Beam path Compressor§OMEGA OMEGA EP OMEGA EP
Compression
Upper 1 to 100 ps Backlighter port
1 to 100 ps
Backlighter port
1 to 100 ps
Lower 20*to 100 ps Backlighter port
20* to 100 ps
Sidelighter port
1 to 100 ps
Beamline
Frequency
conversion
1 ~ to 3 ~
123°port (1 to 10 ns)
48°port (future)
223°port (1 to 10 ns)
48°port (future)
323°port (1 to 10 ns)
48°port (future)
423°port (1 to 10 ns)
48°port (future)
§
Beamline 1 or 2 into either pulse compressor.
*Beams in the lower compressor are limited in energy or pulse width by the B-integral of a
beam combiner optic: a 20-ps pulse width is typical for most applications.

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focused on integrated experiments and developing an improved understanding of physics issues related
to fast ignition (such as the laser-to-electron coupling efciency and electron-beam propagation in high-
conductivity plasmas), benchmarking theoretical models and dening the requirements for full-scale fast
ignition on the NIF. A deliverable of this research is to observe signicant ion heating (more than one
thousand electron volts) and the concomitant increased neutron production in integrated fast-ignition
experiments on OMEGA.
(c) Long-pulse experiments in the OMEGA EP target chamber
When operated in long-pulse mode, the four beams will be used primarily for planar-target
experiments in OMEGA EP’s baseline conguration. The long-pulse beams are frequency converted
from 1~to 3~to improve their coupling efciency to the target. Frequency conversion occurs before
nal transport to eliminate unconverted light before the beams enter the chamber. They are arrayed
at near-normal incidence (23º). It will be possible to extend current OMEGA HED experiments to
higher laser energies and longer pulse lengths. Alternatively, one or two of the beams can be used in
compressed-pulse mode to produce short bursts of hard x rays and/or energetic protons for diagnosing
targets driven by the long-pulse beams. These beams can radiograph targets along and/or perpendicular
to target normal. The OMEGA EP chamber could eventually accommodate experiments in the indirect-
drive conguration with half-hohlraums (hohlraums illuminated from one side), using up to four beams
of variable pulse lengths. For this purpose, the outer cone of beam ports at 48º relative to the hohlraum
axis allow the beams to be incident at an optimum angle for coupling to the hohlraum walls. The 48º
beam cone and options such as frequency converting the beams to 2~provide additional experimental
exibility. Only the 23º UV beams are included in the OMEGA EP baseline design.
(d) Fast-ignition relevant experiments in the OMEGA EP target chamber
The OMEGA EP conguration will permit experiments using various combinations of short-
and long-pulse laser beams to be carried out in the new target chamber, allowing many aspects of high-
intensity and HED physics to be studied. One or two of the new beams will be compressed and will
interact with solid targets or with plasmas produced by two or three long-pulse beams. This will allow
studies of laser and electron beam propagation in plasmas with ignition-scale conductivities. OMEGA
EP is designed to support planar cryogenic target experiments using the OMEGA planar cryogenic target
positioner (not in the baseline).
(e) High-intensity laser–matter interaction experiments in the OMEGA EP target chamber
The compressed petawatt laser beam can be propagated into the OMEGA EP target chamber,
allowing high-intensity laser–matter interaction experiments with intensities in excess of 1020 W/cm2.
1.1.1 High-Power, High-Energy, and Proton-Beam Radiography
The probing of high-energy-density (HED) matter with penetrating x rays or energetic particles
has evolved over the last two decades as the principal technique for measuring the evolution of HED
targets. A large fraction of the HED physics experiments on OMEGA (and on Nova prior to its shutdown)
use drive beams to illuminate a backlighting target, producing x rays to radiograph the primary target.
Thousands of HED backlighting experiments have been performed in the last decade on these and other
facilities, despite the absence of dedicated backlighting laser beams.

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The conventional laser beams on OMEGA and the NIF produce relatively low peak power and
thus suffer several limitations for radiography applications. The primary limitations that are ameliorated
using high-power, short-pulse, high-energy backlighter laser beams such as those available from
OMEGA EP are
(a) The x-ray backlighter power is low. This results in an inability to make the backlighter
brighter than some of the HED physics targets that are at high temperatures themselves
and therefore emitting copious amounts of x rays.
(b) The x-ray photon energies are below ~15 keV, limiting the target thickness or atomic
number that can be radiographed.
(c) The x rays are emitted for the relatively long duration of the laser pulse. This limits the
time resolution Dtand, thus, the image quality that can be achieved. It also impacts the
spatial resolution Dxbecause of motional smearing (given by Dx= vDtfor material that
is moving at velocity v).
(d) Few high-energy protons are produced, limiting the possibility of measuring material
properties other than the x-ray opacity. The ionization state and electromagnetic elds
could be measured with energetic protons.
OMEGA EP will overcome the limitations of backlighting with conventional OMEGA and
NIF beams. It will allow dedicated backlighting beams in both the OMEGA and OMEGA EP target
chambers. The short-pulse capability of illuminating targets at 1020 W/cm2and above allows new regimes
of backlighting and the use of dedicated backlighting beams avoids compromising the symmetry of
implosion experiments on OMEGA.
OMEGA EP will have essentially the same high energy petawatt (HEPW) beam conguration
envisioned for implementation on the NIF advanced radiographic capability (ARC) machine. This will
allow scientists to develop backlighting techniques for use on the NIF by exploiting OMEGA EP’s higher
shot rate and lower shot cost.
1.1.2 HED Backlighting Experiments
OMEGA EP’s enhanced backlighting capabilities will be used for many different experiments.
Examples are described in the following subsections.
1.1.2.1 Cryogenic Implosion Fuel Conditions
The HEPW beams from OMEGA EP backlight OMEGA cryogenic target implosions. The
backlighter must provide sufcient brightness to overcome the implosion self-emission and produce an
image that can be used to infer the density distribution of the hot core with a high signal-to-noise ratio.
Using both of the OMEGA EP short-pulse-capable beamlines, it is possible to irradiate a 50-nm-radius
Si backlighting target at an intensity of 5 #1017 W/cm2using 20-ps pulses. Assuming an efciency of
2 #10–5, this provides ~16 mJ/eV into 4r, which should be sufcient to produce a useful image.

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1.1.2.2 High-Temperature Opacity Measurements
A major application of HED facilities is to measure the opacity of high-temperature materials.
The backlighter brightness needs to exceed that of the high-temperature target. The backlighter spectrum
should also be sufciently at to remove any ambiguities between backlighter and target spectral
features. On OMEGA EP, radiation temperatures signicantly higher than those achieved on OMEGA
would be expected from a 2-kJ, 20-ps beam focused into a small hohlraum. This would be adequate for
developing opacity experiments and the techniques needed for NIF backlighting, as well as performing
opacity measurements on OMEGA.
1.1.3 Fast Ignition
1.1.3.1 Background
Indirect-drive, hot-spot ignition is the baseline approach to achieving ignition and gain on the
NIF, and direct-drive, hot-spot ignition is the main alternative. Fast ignition coupled to a direct-drive or
indirect-drive implosion is a third approach of signicant current interest since it can potentially increase
the target gain or reduce the ignition laser energy requirements. In the fast-ignition concept, the high-
energy driver is used only to compress the fuel without creating a central hot spot. A burning hot spot
is then formed by the rapid deposition of energy into the main fuel. Separation of the formation of the
hot spot from the compression of the main fuel could, if there are no unexpected physics issues, reduce
the energy requirement of the driver.
Fast ignition would make high-gain applications with drivers that have less energy than the full
NIF (but more than OMEGA) possible and may relax requirements on efciency and drive symmetry. Fast
ignition can also be used with drivers such as ion-beam or Z-pinch radiation sources that can compress
thermonuclear fuel to a high density. The science of fast ignition is more complex and less mature than
central hot-spot ignition, so experimental tests under plasma conditions close to fast-ignition conditions
are crucial. OMEGA EP will be the best-suited facility to perform the most important fast-ignition
experiments because of OMEGA’s unique ability to compress cryogenic targets.
For ignition, the energy Erequired to be deposited by a fast-ignition beam is E= 140 (100/t)1.8 kJ,
where tis the fuel density in g/cm3. Consequently, fast ignition is unlikely to be achieved with OMEGA
EP since the current estimate is that ~100 kJ in 10 ps is required in the high-intensity beams. The main
uncertainty in this estimate is the coupling of absorbed laser energy to the compressed core. The hot-
electron temperature (the average particle energy) generated by the HEPW beam is readily estimated to
be ~1 MeV for the electrons to be stopped efciently in an areal density of a few hundred mg/cm2, as
required for hot-spot formation. This areal density is approximately equal to the range of alpha particles
in the hot spot.
Hydrodynamic simulations have been used with considerable success to model “traditional” ICF
implosions. Existing software codes, however, are inadequate for fast-ignition design, and more complex
models, including physical phenomena that are, at present, poorly understood, need to be developed. It is
currently believed that 3-D hybrid codes with particles for the fast electrons and uids for the background
are required and that magnetic-eld generation and neutralizing reverse current will be important.

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1.1.3.2 OMEGA EP Fast-Ignition Program
The key experiments needed to demonstrate the fast-ignition concept and determine the optimum
parameters for the NIF will be carried out on OMEGA and OMEGA EP. The fundamental goal is to
determine the coupling of the HEPW beam energy to the compressed core of a cryogenic implosion.
Experiments will include the propagation of the high-intensity laser beam in the target, the conversion
efciency of the laser light to hot electrons (or ions), the intensity scaling of the hot-particle energy, the
transport of these particles, and the heating of the compressed core.
1.1.3.2.1 Intensity Scaling of Hot-Electron Energy
The coupling efciency to DT or plastic targets may be different than for high-Ztargets and is
a major uncertainty in the fast-ignition scheme. In addition, the relationship between the hot-electron
temperature Thot and the ponderomotive potential Upond of the high-intensity beam appears to be a
function of target Z. This will be determined experimentally in planar cryogenic target experiments in
the OMEGA EP target chamber. The beam intensity will be varied by changing the compressed pulse
duration in the 1- to 10-ps range.
1.1.3.2.2 Electron-Beam Transport
HEPW-generated electron-beam propagation without excessive divergence is important for
fast ignition. For example, the compressed core on OMEGA is only ~80 nm in diameter and remains
assembled for less than ~100 ps, dictating a tight specication on the pointing accuracy of the channeling
and ignitor beams. At the same time, the critical-electron-density (nc) contour for 1-nm light has a
430-nm radius while the 10 nccontour has a 150-nm radius. From this approximate characterization of
the radial density prole, it is clear that the propagation of the high-intensity beams through the overdense
plasma region requires good collimation and directionality of the electron beam that is generated at the
end of the laser propagation. Studies of these processes will be carried out in the OMEGA EP chamber
followed by full-scale, integrated implosion experiments in the OMEGA chamber with the compressed
OMEGA EP beams used as the channeling and ignitor beams. The cone-in-shell fast-ignitor concept
will also be validated.
1.1.4 SSP-Related High-Energy-Density Physics
Areas of high-energy-density physics of interest to NNSA’s Stockpile Stewardship Program (SSP)
include (1) dynamic materials studies, including high-pressure equation-of-state (EOS) experiments of
materials at high energy density, and (2) compressible hydrodynamics and radiative hydrodynamics
experiments. The OMEGA EP target chamber design is optimal for both classes of experiments because
all the laser energy is incident from one direction. The ability to heat compressed materials with high-
intensity beams and the advanced radiographic capabilities are equally valuable.
A related area is the study of matter near and above solid density at temperatures that can vary
from a few electron volts to several hundred electron volts. There are applications in planetary and
earth sciences, in addition to ICF and HED physics, including studies of the EOS and other materials
properties relevant to high-pressure planetary interiors. Challenges presented by this eld include
producing controlled conditions and their diagnosis. A number of complementary techniques can be
used on OMEGA EP to access these conditions.

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2Ya. B. Zel’dovich and Yu. P. Raizer, “Thermal Radiation and Radiant Heat Exchange in a Medium,” in Physics of Shock
Waves and High-Temperature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein (Academic Press,
New York, 1966), Chap. II, Vol. I, pp. 107–175.
(a) A strong shock wave may be sent through a sample using the long-pulse UV beams. This
method is extensively used for EOS experiments but it allows one to access points on the
principal Hugoniot only.
(b) Isentropic (shockless) compression can be achieved with a carefully shaped pressure drive
coupled to the appropriate target design. This method permits access to the high-density,
low-temperature region of phase space that is of special relevance for geophysical and
planetary science problems and the study of metallic hydrogen.
(c) The target may be heated isochorically by penetrating radiation, with little decompression,
to access the solid-density, high-temperature, high-pressure region of phase space. The
penetrating radiation can be hard x rays, fast electrons, or fast protons produced during
the interaction of a short, high-intensity laser pulse with matter, or thermal conduction
resulting from ultrafast-laser absorption in the plasma corona. This method allows the
opacities of partially and fully degenerate matter (warm dense matter) to be studied.
1.1.4.1 Equation of State Measurements of Materials
Knowledge of the EOS of materials, including those used in above ground experiments (AGEX), is
of paramount importance to the SSP. Many conditions of interest require shock waves driven at megabar
pressures, and the EOS of materials at these pressures is often unknown.
The OMEGA EP system will signicantly extend the range of conditions and materials that can
be tested with OMEGA because of the higher laser-driver energy and the increased number of shots
available. The OMEGA EP target chamber will be congured to accommodate a VISAR1(velocity
interferometer system for any reector) diagnostic to determine the EOS and will be compatible with
the OMEGA planar cryogenic target positioner.
These experiments make use of the “impedance matching” method described in Zel’dovich and
Raizer.2A reference material with a known EOS is placed next to a material of unknown EOS, and a shock
wave is propagated from the former material to the latter. Measurements of the shock speeds through the
two materials allow inference of the pressure and particle velocity in the material of unknown EOS.
EOS experiments on OMEGA EP will involve the use of all four UV beams to drive a package
or three UV beams for the drive and one as a backlighter. There is interest in EOS data at pressures
from kilobars to tens or hundreds of megabars, requiring intensities in the range of 1011 to 1016 W/cm2.
A nominal 1-mm-diam spot sufces for most of these experiments, but the extreme intensities require
spots ranging from 0.5 to 3 mm in diameter. Drive pulses are typically square in time and range from 1
to 10 ns in duration. The packages have various types of shields (typically with a 10-mm diameter). The
target thicknesses (ablator plus pusher plus sample) are of the order of a few hundred microns, and the
individual component thicknesses are determined by the shock dynamics (rarefaction and reverberation)
to produce steady and planar conditions in the sample. OMEGA EP will allow for the use of phase
plates, although none are included in the baseline project.
1Note that VISAR is not a baseline diagnostic for OMEGA EP, but it could be implemented.

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In addition to the VISAR diagnostic that views the target along its rear axis (normal), a backlighter
target (>10 mm to the side) produces x-rays that radiograph the target side-on. An x-ray streak camera
(opposing the backlighter) detects these x-rays to view the motion of the pusher. For thick packages,
the shock continues to propagate for many nanoseconds after the laser pulse has ended. OMEGA EP
includes orthogonal viewing angles.
1.1.4.2 Isentropic Compression
Isentropic (shockless) compression will be used to reach the high-density, low-temperature region
of phase space that is of special relevance for geophysical and planetary science problems and for the
study of metallic hydrogen. To maintain the desired low temperature of the sample, a long, carefully
shaped pressure drive is required. With the long pulse duration, high energy, and individual pulse shaping
and timing available for each of the OMEGA EP beams, it will be possible to provide samples in a new
and unexplored temperature and density range.
1.1.4.3 Isochoric Heating Experiments
Fast electrons or protons generated by an ultrashort laser pulse can be used to isochorically heat
samples at solid density, high temperature, and high pressure. Generally, the pulse duration of the fast
electrons produced in the interaction of a high-intensity short-pulse laser with matter is close to the laser
pulse duration. At relativistic intensities Isuch that Im2> 1018 W/cm2, where mis the laser wavelength
in microns, the electrons are emitted into a cone with a half-angle <40º in the forward direction, and
the effective temperature of the electrons is, to a good approximation, proportional to the laser intensity
(Thot ?Im2). The short-pulse duration of <10 ps minimizes the hydrodynamic expansion of the sample
and makes the heating close to isochoric. It will be possible to study the opacities of warm, dense matter
using diagnostic techniques such as absorption spectroscopy with a spectrally broad backlighter produced
by the second short-pulse beam.
1.1.4.4 Hydrodynamic Instability Experiments
The nonlinear evolution of Rayleigh–Taylor and other hydrodynamic instabilities remains an
important SSP problem. A quantitative description of the evolution of the bubbles and spikes in the highly
nonlinear phase of implosions is essential. To address this issue, an embedded-interface, Rayleigh–Taylor
test bed that has linear growth factors in excess of 1000 is being developed for OMEGA. On OMEGA
EP, the higher energy and longer pulses available to accelerate a planar package will extend these
experiments to still larger growth factors, allowing the highly nonlinear development of the instability
at the embedded interface to be studied. In particular, the nonlinear mixing and the bubble-and-spike
growth characteristics will be studied for both single-mode and multimode perturbations.
The evolution of Rayleigh–Taylor instability at an interface can be studied either by accelerating
a target with the laser ablation of material or by decelerating a target in a background medium. This
research has been started on the OMEGA Laser System with a focus on experiments using a decelerating
target. No correction for ablation is needed with a decelerating foil, and the growth can be calculated
with the classical formula.
Both large-area backlighting and point-projection backlighting are possible. Large-area
backlighting needs several kilojoules of laser energy at a pulse length of ~1 ns to illuminate the large-
area x-ray source. The backlighter needs to be independently timed, with delays from ~0.3 to 100 ns
relative to the drive beam. Point-projection backlighting is more energy efcient and needs only ~500 J,

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G6335bJ2
Figure 1.1
A simplied view of the OMEGA EP
Laser Bay showing the four beamlines,
grating compressor chamber, target area
structure, and target chamber relative to
the OMEGA Laser System.
but requires the short-pulse duration of <100 ps available on OMEGA EP. Alternative experimental
congurations producing 2~or 3~beams are available design options.
1.1.4.5 Indirect-Drive Experiments
OMEGA EP will have the capability of irradiating targets with beams at 48º to the target normal
even though it is not included in the baseline project. This is ideal for the irradiation of half-hohlraums
with >20 kJ of laser energy in pulses up to 10 ns. While no specic experiments are yet designed, it is
likely that this capability will be of signicant interest to the national laboratories and will be developed
when the facility becomes available for target physics experiments.
1.2 S C
The new laser facility is housed in a structure attached to the south side of the existing LLE
building (see Fig. 1.1). The OMEGA EP target chamber is due east of the existing OMEGA target
chamber. The most signicant structural feature of the OMEGA EP Laser System is an 83-ft-wide,
263-ft-long, and one-story-high (14-ft) concrete box-beam, which serves as a rigid “optical table.” The
rst and second oors of the structure serve as the optical table and are 30-in.-thick concrete slabs.
The lower oor rests on a bed of compacted gravel and is structurally independent from the laboratory
building that encloses it. This structural approach was based on the success of the original OMEGA
facility design. It provides the high degree of vibration isolation that is necessary for precision laser
operations. The area inside the box-beam on the lower level contains the Diagnostic Bays, the Sources
Bay, and two Capacitor Bays, that house the power conditioning system that powers the laser ampliers.
The Sources and Laser Bays are climate controlled and designed to operate as Class-1000 clean rooms,
but actually perform to nearly Class-100 conditions. A Control Room on the second oor is provided to
the east of the Laser Bay with a viewing gallery at the north end of the Laser Bay.
Four laser beamlines (two short/long-pulse beams and two long-pulse beams), arranged
horizontally across the oor, are located to the south of the grating compression chamber (GCC) and the
target chamber and its supporting structure. Beams 1 and 2 may be temporally compressed to short-pulse
IR beams in the GCC and then propagated into either target chamber. Alternatively, all four beams may
be operated in long-pulse mode, frequency tripled, and directed into the OMEGA EP target chamber.

V VII–S D
OMEGA EP O M
P 10 of 35
A schematic diagram of the main components of a beamline is shown in Fig. 1.2. Each beamline
is “folded” into two levels: an upper level that includes a 7-disk booster amplier and transport spatial
lter (TSF) and a lower level that forms a cavity between the cavity end mirror (CEM) to the south and
the deformable mirror (DM). The cavity includes an 11-disk main amplier, a cavity spatial lter (CSF),
and a plasma electrode Pockels cell (PEPC). The DM corrects wavefront errors in the laser pulse that
originate from optical aberrations in the optics or from prompt-induced distortion of the laser disks
produced when the ampliers re. The PEPC is an electro-optical switch using polarization rotation to
trap the laser pulse in the cavity, providing an additional pass through the main amplier resulting in
higher gain.
The seed laser pulse (generated in Laser Sources) is injected into the transport spatial lter via
a periscope. For short-pulse experiments in either target chamber, the seed pulses of Beams 1 and 2
are generated using optical parametric chirped-pulse amplication (OPCPA). The injected pulse passes
through the booster amplier and is reected off the fold mirror to the polarizer (POL1) and into the main
amplier. The pulse makes either one or two round-trips through the cavity to gain the required energy,
then returns through the booster amplier and TSF, and propagates to a switchyard. In the switchyard,
the beam is directed into the GCC for temporal-pulse compression or to the frequency-conversion
crystals (FCC’s) for the generation of long-pulse UV beams. A second polarizer (POL2 of Fig. 1.2) is
inserted between the PEPC and the CSF to prevent light reected from the target from damaging the
main amplier. Details of its use are explained in Sec. 1.5.
Figure 1.2
Optical components for the injection and amplication portions of an OMEGA EP beamline. Beamlines 3 and 4 do not
have short-pulse capability and therefore do not require POL2.
Injection lens
From
laser
sources Up-collimator Pointing/centering
mirrors
Vacuum window Diagnostic
beamsplitter
To compressor
or FCC’s
Transport spatial lter
7-disk
booster amplier
Fold
mirror
Cavity
end mirror
POL1
PEPC
Rejected
light
Cavity spatial lter
11-disk
main amplier Deformable
mirror
G5221cJ2
POL2*
45 m
23 m
*Used in beamlines 1 and 2 only

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G6860J1
TGA 2 TGA 3
TGA 1 TGA 4 Input beam Beam combiner
Figure 1.3
The upper of two four-grating pulse compressors is shown inside the GCC. The lower compressor is identical. The output of
each compressor is directed to a beam combiner where the pulses are coaxially aligned. A target chamber selection mirror
(not shown) diverts pulses to either target chamber. Alternatively, the two pulses can be used to simultaneously backlight
and sidelight an OMEGA EP target.
Each temporally stretched pulse is compressed to the desired pulse width while maintaining
beam size using a pulse compressor comprised of a quad of tiled multilayer dielectric diffraction (MLD)
grating assemblies. The two pulse compressors are located in the GCC aligned atop one another, and
the upper compressor is illustrated in Fig. 1.3. The principle of pulse compression is based upon the
diffraction of light off the grating surface and the fact that different wavelengths of light travel different
distances within the compressor before being recombined at Grating 4.
After pulse compression, the beams can be directed to either the OMEGA or OMEGA EP target
chamber. When the beams propagate to the OMEGA target chamber, they are coaxially aligned using a
beam combining optic and a target chamber selection mirror directs them to the target chamber. They
enter the chamber through diagnostic hex port (H9) and traverse the chamber to hex port (H7) where
an off-axis f/1.8 parabolic mirror focuses them onto the target. The focal spot can be shifted to any
location within 1 cm of the center of the chamber to provide for exible backlighting geometries. The
foci of the two beams may be separated by ~1 mm.
In OMEGA EP, two beam congurations are possible. In the rst conguration, the beams
propagate along the backlighter beam path, enter the target chamber through port 33, and are focused
by an f/1.8 off-axis parabolic mirror in a nearly opposing port that focuses the beam onto the target. The
beams may be coaxially aligned in this setup. In the second conguration, the two beams can propagate
separately along the backlighter and sidelighter paths, entering the chamber through ports 33 and 69.
They are similarly focused by a pair of f/1.8 off-axis parabolas on nearly opposing ports. The focal spots
of these beams can be shifted to any location within 1 cm of target chamber center, providing for exible
experimental geometries and congurations. An illustration of the concept is shown in Fig. 1.4.
In long-pulse mode, all four beams are diverted in the switchyard to the frequency-conversion
crystals, where they are frequency tripled to the UV (351 nm). UV high-reector (HR) mirrors and a
focus lens (FOA) deliver the beams to the target chamber at 23º relative to the target normal. These
UV-only mirrors also serve to separate unconverted IR and second-harmonic light before the beam
enters the target chamber. A future option is to add a 48º beam path relative to target normal. The
four (or eight) ports for the UV beams straddle the f/1.8 off-axis parabola for symmetric production of
preformed plasma.

V VII–S D
OMEGA EP O M
P 12 of 35
The system is congurable so that Beamlines 1 and/or 2 may operate in short- or long-pulse
mode while Beamlines 3 and/or 4 operate in long-pulse mode since each beamline has its own seed
pulse. Beams 3 and 4 cannot be directed to the OMEGA target chamber.
1.3 S P S
1.3.1 Short-Pulse Performance
The short-pulse beams are capable of compression to various pulse widths in the range of 1 to
100 ps. The top-level specications for these beams are given in Table 1.2. Beam performance parameters
are given for (1) the maximum on-target intensity, (2) the 10-ps fast ignitor, and (3) the copropagated
channeling beam. For the baseline design, peak focused intensities of >1019 W/cm2(using f/1.8 reective
optics) are available at the shortest pulse width. For short-pulse backlighting, the pulse width chosen
will depend on the needs of the specic experiment.
The numbers quoted in Table 1.2 assume a system performance limited by the damage threshold
of the multilayer dielectric reection gratings. The use of improved grating technology provides up to
~2.6 kJ of laser energy per beam. The pulse width of Beam 2, when copropagating with Beam 1, is limited
by the B-integral accumulated while it passes through the beam combiner in the grating compressor
chamber, resulting in a maximum on-target intensity of ~4 #1018 W/cm2. For the normal operations,
the pulse width should be ~35 ps to obtain the minimum focal spot size, but a 20-ps pulse is possible for
experiments requiring a larger focal spot. The performance in short-pulse mode is strictly limited by the
damage uence of the MLD compression gratings. The laser itself, even at the relatively short output-
G6861J1
Figure 1.4
Cutaway illustration of the OMEGA EP target chamber (TC) and the GCC (partial view) looking south. The TC selection
mirror (upper right) can be aligned to direct the temporally compressed beam to enter the backlighter port (blue) or sidelighter
port (red). A related geometry enables simultaneous backlighting and sidelighting within the OMEGA EP chamber. The
TC selection mirror may also be reoriented to direct the beam to the OMEGA TC (not shown).

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Table 1.2: Specications for the 1053-nm chirped-pulse-amplication beams. Note
that the beams can be used for backlighting at all pulse widths from the
minimum shown up to 100 ps. When Beam 2 is not copropagating with
Beam 1, it has the same parameters as Beam 1.
Beam 1 Beam 2
Baseline performance
Maximum
intensity
Fast-ignitor
beam
Channeling beam
copropagated
Pulse width (ps) 1 10 100
Focal spot radius (nm) 10 10 20
Energy on target (kJ) 0.8 2.6 2.6
Intensity (W/cm2) ~2 #1020 ~6 #1019 ~3 #1018(a)
(a)Limited by B-integral in beam combiner.
stretched pulse length of 1.13 ns, is capable of producing >4.0 kJ of energy at the input to the compressor.
The nal grating (G4) is critical as it sees the fully compressed pulse and will damage rst.
1.3.2 Long-Pulse Performance
Anticipated performance parameters of the four long-pulse beams are given in Table 1.3. The
UV on-target energies are derived from a conservative scenario in which the IR energy at each pulse
width is limited to 80% of the NIF design value. To allow for possible inhomogeneities in the frequency-
conversion crystals or alignment errors, the frequency-conversion efciency is de-rated by 10% from
the calculated value, and the transport from the frequency-conversion crystals to the target (including a
4% diagnostic pickoff) is conservatively assumed to be 85%. The calculations used for Table 1.3 assume
low-risk, existing technologies and demonstrated UV damage uences for optical coatings. In spite
of the de-rating of OMEGA EP energies relative to NIF design values, the OMEGA EP performance
requirement of 5 kJ/beam is met.
The performance of the laser chain for 1- and 10-ns square pulses is limited by the peak uences
and damage limits of the optical components in the OMEGA EP beamline after the last pass through
the cavity, the booster-amplier section, and the UV transport to target. The most damage-threatened
components in the UV subsystem in both the 1-ns and 10-ns cases are the UV transport mirrors.
Careful image relaying to the plane of the rst UV transport mirror is necessary to ensure optimal
system performance. The next most threatened UV component is the output surface of the FCC’s. In
the IR sections, the cavity polarizer in reection is the most damage-threatened component. The limit
at 10 ns corresponds to the maximum pulse width that can be produced by the current front-end sources
design.
Table 1.3 also lists the UV energy potential of the system, assuming a modest increase in the
current coating damage uence. The long-pulse performance of OMEGA EP for pulses ≤1 ns is limited
by the accumulated B-integral in the UV subsystem (which is held to ≤2). For pulse lengths longer than
~1 ns, the performance is limited by the damage uence of current UV high-reector coatings. This
scales with Gaussian pulse width xas 5.2 x1/3 J/cm2, with xmeasured in nanoseconds.

V VII–S D
OMEGA EP O M
P 14 of 35
1.4 L S S
The Laser Sources Bay is located between the north and south Capacitor Bays on the rst oor
of the facility. Each beamline in OMEGA EP has its own dedicated set of laser drivers, referred to as
laser sources. Beamlines 1 and 2 have the capability to produce both short- or long-pulse seed pulses
for their dedicated beamline. Thus, there are six independent laser sources.
1.4.1 Laser Sources 1 and 2
Different architectures are used for generating the long-pulse and short-pulse laser sources, as
indicated schematically in Figs. 1.5 and 1.6. The long-pulse (LP) source is largely based on existing
OMEGA technology with some modications made to the regen to allow for 10-ns pulses. The short-pulse
source is based on optical parametric chirped-pulse amplication (OPCPA) because existing long-pulse
technology lacks the bandwidth needed.
The short-pulse beams start with a commercial Time Bandwidth Products mode-locked oscillator
that produces pulses with an ~200-fs duration. These pulses are stretched to ~2.4 ns (FWHM) in an optical
system that uses a diffraction grating to impose different delays on different frequency components.
The resulting “chirped” beam is spatially shaped before being amplied using an optical parametric
amplier. This OPCPA stage is critical to the performance of the short-pulse beams. Attractive features
of OPCPA include a broad gain bandwidth, high gain in a short optical path, and reduced amplied
spontaneous emission. These are exploited to preserve the bandwidth of the signal beam and provide a
gain of ~109.
Optical parametric amplication is a nonlinear optical process whereby energy is down-converted
from a (pump) beam of higher frequency into two beams of lower frequency, known as the signal and
idler beams. For OMEGA EP, the pump beam is a frequency-doubled, 527-nm-wavelength, Nd:YLF laser.
LBO (lithium tri-borate) crystals are used as the parametric-amplication media. The signal beam is
the input to the OPCPA stage, and the amplied signal beam is the output. The idler (1053 nm, like the
signal) is generated in the LBO crystals and separated after the OPCPA stage. The sum of the (chirped)
Table 1.3: Performance parameters of the 351-nm long-pulse beams (quantities refer to a
single beam). The “baseline” UV energies are what can be obtained with exist-
ing technology. The “potential” UV energies are possible with reasonable optical
technology developments. The quoted intensities are averages over the focal spot
and use the “baseline” UV energies.
Square pulse width (ns) 0.1 1.0 4.0 8.0 10.0
UV on-target energy (kJ):
Baseline
Potential
0.25
0.25
2.5
2.5
3.7
4.8
4.5
6.0
5.0
6.5
Intensity (W/cm2)
for 1-mm spot diameter 3 #1014 3 #1014 1.2 #1014 7 #1013 6 #1013
Intensity (W/cm2)
for 100-nm spot diameter 3 #1016 3 #1016 1.2 #1016 7 #1015 6 #1015

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Figure 1.5
Schematic diagram of the Laser Sources subsystem design for sources 1 and 2. These sources support both short-pulse (1 to
100 ps) and long-pulse (1 to 10 ns) operation. The “green” coloration from the CLARA SHG indicates 2~. Beamlines 3
and 4 do not have short-pulse capability and therefore have a different conguration.
Figure 1.6
Block diagram of the Laser Sources Beamlines 3 and 4. These sources do not have short-pulse capability. Pulse lengths
and shaping between 1 and 10 ns are provided. The regen in these systems limits the pulse width.
signal and idler frequencies equals the pump frequency for each temporal portion of the pulse. Optical
parametric amplication is essentially the reverse of sum-frequency mixing, where two lower frequencies
combine to form a higher frequency as in the frequency-conversion crystals, and is described by the
same equations. OPCPA is a special case of optical parametric amplication where the signal beam is
frequency chirped.
The OPCPA pump laser starts with the same components as the long-pulse beam up to and
including the spatial shaping stage. It also includes a high-repetition-rate (5-Hz) crystal large aperture
ring amplier (CLARA) that amplies the shaped IR pulse to ~3 J/pulse and a second harmonic generator
(SHG) that produces ~2-J 2~pulses that are square in space and time. The signal emerging from the
OPCPA stage is further amplied using the same 15-cm Nd:glass amplier that is used in long-pulse
G6862J1
Short-pulse
oscillator Stretcher OPCPA
stage 2
OPCPA output
spatial filter
Short pulse
apodizer
Apodizer output
spatial filter
Long-pulse
beam shaper
Long-pulse
preamplifier
Phase
modulator
Long-pulse
apodizer
Regen
CLARA
Beamline
injection
Periscope to
Laser Bay
Discrete zoom
spatial filter
Isolation
stage
15-cm glass
amplifier
OPCPA
stage 1
Second harmonic
generator (SHG)
Aperture coupled
strip line (ACSL)
Integrated front end
source (IFES)
Short-Pulse Generation Chain
Long-Pulse Generation Chain
G6863J1
Beam
shaper
Phase
modulator
Apodizer
Regen
Integrated front end
source (IFES)
Beamline
injection
Periscope
to Laser Bay
Discrete zoom
spatial filter
Isolation
stage
Power
amplifier
Aperture-coupled
strip line (ACSL)

V VII–S D
OMEGA EP O M
P 16 of 35
mode. The output of the OPCPA stage can also be propagated through the main portion of the laser
system to establish optical alignment, verify compressor performance, and align the beam transport
and focusing systems.
The long-pulse mode of Sources 1 and 2 use the same technologies as Sources 3 and 4 described
in Sec. 1.4.2 below.
1.4.2 Laser Sources 3 and 4
In long-pulse mode, the beam pulse lengths are adjustable between 1 and 10 ns. A schematic
diagram of the system is shown in Fig. 1.6. The laser pulse originates from an integrated front-end source
(IFES) that contains a commercial distributed feedback ber laser (Koheras). The IFES produces a
continuous wave output (1053.044 nm) that is subsequently shaped so that the desired on-target temporal
prole will be generated after the nonlinear processes of amplication and frequency conversion. The
pulse-shaping system uses either aperture-coupled strip line (ACSL) or arbitrary-waveform-generator
(AWG) technology, depending on the pulse length and bandwidth requirements for a given experiment.
The temporally shaped pulse is amplied in a regenerative amplier that produces ~5-mJ laser pulses
at 5 Hz. An apodizer is then used to shape the spatial prole of the beam from round to square, creating
an optimized, on-target, UV spatial prole. Next, a small amount of frequency-modulation bandwidth
is imposed to suppress stimulated Brillouin scattering that could otherwise threaten large optics such
as the focus lenses. The bandwidth of 0.5 Å (~15 GHz) is applied at a modulation frequency of 3 GHz
using a bulk microwave lithium niobate (LiNBO3) modulator. The pulse is further amplied in a glass
amplier before injection into the transport spatial lter of the beamlines. The optical-image plane of
the LP apodizer is relayed throughout the system. The output of the long-pulse front-end source is a
spatially square, temporally shaped beam with a nearly at wavefront.
1.5 L B C
The optical components in the injection and amplication portions of one beamline are almost
the same regardless of whether a long pulse or a short pulse is passing through. Referring to Fig. 1.2,
the input laser beam (~280 mJ for long pulses and up to 5 J for short pulses) is injected by an injection
mirror and color-corrected injection lenses into the TSF, where it expands to an ~37-cm-sq aperture. For
short pulses, more of the system gain is placed at the front end of the system, where there is the most
gain bandwidth. In long-pulse operation, multiple passes through the amplier make up for the lower
input energy.
After the expanded beam makes an initial pass through the seven-disk booster amplier, it is
reected 180º by a fold mirror and the Brewster’s angle polarizer (POL1) to enter the main laser cavity
at a level 1.5 m lower. This represents a layout change from the NIF to t the beamlines into a smaller
building. As a result, the focal length of the TSF is shorter than the NIF TSF. This change also results
in a smaller fold mirror and a different coating requirement for this mirror because of the reduced angle
of incidence.
The beam must be p-polarized relative to the disks in both ampliers. The amplier disks are
mounted lengthwise on edge to minimize stress, requiring a horizontal orientation of the electric eld.
The electric eld is therefore s-polarized relative to the fold mirror and Brewster’s polarizer POL1,
resulting in maximum reectance from the polarizer surface.

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To permit four passes through the main amplier, the polarization of the beam must be rotated
to prevent the beam from being reected out of the cavity following the second pass. The PEPC is used
to accomplish this. It is an electro-optic device developed at LLNL that rotates the electric-eld vector
of plane-polarized radiation by 90º. For four-pass operation, the PEPC is initially in its “off” state. After
the pulse has passed through the PEPC, the device is switched to its “on” state by applying a high voltage
(~20 kV). The returning beam is then rotated to a vertical polarization state, making it p-polarized relative
to the Brewster’s angle polarizer POL1, resulting in high transmission through the polarizer. The beam
then reects from the cavity end mirror and returns through the polarizer and the “on” PEPC. The PEPC
rotates the beam’s polarization another 90º back to its initial, horizontal orientation. The voltage on the
PEPC is then turned off, and, following the fourth pass, the beam is switched out of the cavity by POL1
and returns to the upper beamline.
The net small-signal gain through the main and booster ampliers is ~105. The deformable mirror
at one end of the laser cavity corrects for low-spatial frequency aberrations (of length scale ≥33 mm)
introduced by the amplier disks. A sample of the output beam immediately after the TSF is deected
to a Shack–Hartmann wavefront sensor. The output of the wavefront sensor is used to generate error-
correction signals sent to each of 39 actuators on the deformable mirror.
The cavity and transport spatial lters each use a pair of aspheric lenses housed at the ends of
evacuated tube assemblies to spatially lter the light between amplier passes and to provide relay-plane
imaging. The cavity spatial lter relays the image plane of the front-end apodizer to the deformable
mirror. North of the TSF assembly there is a diagnostic beamsplitter mirror (DBS) to provide a path to
beam diagnostics and alignment packages.
In both the cavity and transport spatial lters, the beam passes through a different pinhole on each
pass through the spatial-lter focal plane. This “angular multiplexing” reduces the likelihood of pinhole
closure in the cavity spatial lter, where there are four pinholes in an assembly, one for each pass. Angular
multiplexing is used in the TSF to allow the seed beam to be injected into the main beamline.
To permit two passes through the main amplier, the polarization of the beam does not need
to be rotated to prevent the beam from being reected out of the cavity following the second pass. The
PEPC remains in its passive state while the pulse is in the cavity so that the pulse exits the cavity after
its second pass. A second Brewster’s angle polarizer (POL2) is inserted in the cavity during short-pulse
operation, oriented 90º in azimuth from POL1, so that light will be transmitted when the PEPC is “off.”
In conjunction with the PEPC, POL2 provides a simple means of preventing back-reected pulses from
the target from re-entering the main amplier. (Pulses back-reected from the target could extract gain
from the ampliers and damage the injection mirror in the TSF.) The PEPC is pulsed “on” just after
the main pulse exits the cavity. Back-reected light that has re-entered the beamline has its polarization
rotated by the PEPC and is rejected from the system by POL2 into a beam dump before it can reach the
main amplier disks and deformable mirror.
This second polarizer is only used when the beam is operated in short-pulse mode (two or four
pass), when there is a risk of IR light being back-reected from the target. In long-pulse mode, any UV
light reected from the target cannot pass the IR transport mirror and cannot re-enter the beamline.
POL23is removed from the cavity to avoid damage in this mode of operation. Insertion of POL2 into the
cavity introduces a shift in the beam centerline that is compensated for by the insertion of an oppositely
3Note: Only the short-pulse Beamlines 1 and 2 have the second polarizer (POL2).

V VII–S D
OMEGA EP O M
P 18 of 35
G6967J1
Upper
compressor
OMEGA EP grating compressor chamber Target chambers
Beam
combiner
TC
selector
Lower
compressor
Sidelighter
periscope Sidelighter
Backlighter
OMEGA
OMEGA EP
oriented Brewster’s angle plate or polarizer. Support structures mounted on the laser bay oor house the
fold mirror, the PEPC, polarizers, and the cavity end mirror.
The components of the beamline are interconnected with nitrogen-lled beam tubes. The nitrogen
in these tubes prevents oxygen from degrading the internal silver reecting surfaces of the ampliers
at the ends of the main and booster ampliers and maintains the low-percent RH working environment
required by the coatings on the polarizers. The tubes and ampliers are positively pressurized to ~0.1 in.
of H2O and a temperature, percent-oxygen and percent-RH monitoring system provides an out-of-
specication alarm in the Control Room.
1.5.1 Beam Transport
Depending on the individual beamline and experimental conditions, the amplied pulse emerging
from the transport spatial lter may take one of several paths, as shown in Fig. 1.7. For short-pulse
experiments, Beam 1 or Beam 2 may be routed to the upper or lower compressor in the GCC, where
four matched MLD tiled grating assemblies temporally compress the pulse. A deformable mirror after
the fourth tiled grating assembly provides static wavefront correction. After passing through individual
compressors, the beams are co-aligned through a polarizing beam splitter called the beam combiner.
Beam 1 is reected off this optic in s-polarization while Beam 2 is transmitted in p-polarization. The
co-aligned beams are routed to one of the target chambers using the target chamber selection mirror
and focused using an f/1.8 off-axis parabolic mirror. Transport from the GCC is in an evacuated beam
transport tube connected to the target chamber being used.
Alternatively, after the compressed pulses reect off their respective DM, the beams may be
independently and simultaneously directed to the OMEGA EP backlighter and sidelighter (see Fig. 1.4).
The beam from the upper compressor may be directed to the backlighter and the beam from the lower
compressor may be sent to the sidelighter. This capability allows for stereoscopic viewing of target
experiments. This capability does not exist for the OMEGA target chamber as there is only one beam
transport tube. The ow chart below and Fig. 1.7 illustrate this concept.