Leonid E. Zakharov's Web Page
I am a Principal Research Physicist at the Princeton Plasma Physics
Laboratory (Room A130). You can reach me at
zakharov@pppl.gov
t.n. 609-243-2630
fax 609-243-2662
Leonid E. Zakharov
Princeton Plasma Physics Laboratory
MS27
P.O. Box 451
Princeton, NJ 08543
---Material on this web page is organized in
the
inverse
chronological order---
(the title
and
the marker .ps are linked to the original .ps file, the marker
.pdf is
linked to the derived .pdf-file, the markers .ps2, .pdf2 are
linked to
compact 2viewgraths/per page versions. .ps, .ps2 files can be big)
2009 2008 2007
2006
2005
2004 2003 2002
2001 2000 1999
Numerical codes and
the
theory.
Real Time
Forecast (RTF) of tokamak discharges
The theory of Equilibrium reconstruction
Equibrium
and associated codes for
download:
Cbbsh
ESI
ESC
NGS
2011, September
21, - "Scalable
Flowing Liquid Lithium (FLiLi) system", .pdf
file
27.6 MB movie Alcohol/Copper
Prototype of FLiLi, fabricated by the author.
A practical
system for implementation of a flowing plasma pumping liquid
lithium layer (FLiLi) in tokamaks is proposed. The suggested
scheme suggests a unique approach for power extraction from
tokamaks, which combines a new high performance regime (called
LiWall Fusion regime and associated with efficient pumping of
plasma particle by flowing lithium) with a heat sink (actively
cooled by He gas with expected power extraction rate of 10
- 15 MW/m2 at relatively low gas temperature 300o C).
The FLiLi
system conceptually resolves the issue of maintaining the plasma
facing lithium surface clean and insensitive to the in-vessel
tokamak environment.
2009, April
24, -KSTAR
Seminar, National
Fusion Research Institute, Daejeon, Korea. "The
basics
of the LiWall Fusion (LiWF) concept", .pdf
file and compact
.pdf2
file.
The presently
adopted plasma physics concept of magnetic fusion has been
originated
from the idea of providing low plasma edge temperature as a
condition
for plasma-material interaction. During 30-years of its
existence this
concept has shown to be not only incapable of addressing
practical reactor development needs, but also to be in conflict
with
fundamental science of a stationary and stable plasma.
Meanwhile, the demonstration of exceptional pumping capabilities
of
lithium surfaces on T-11M (1998), discovery of the quiescent
H-mode
regime on DIII-D (2000), and a 4 fold enhancement of the energy
confinement time in CDX-U tokamak with lithium (2005),
contributed to a
new vision of fusion relying on high edge plasma temperature.
The new
concept, called LiWalls, provides a scientific basis for
developing
controlled fusion as a component of the nuclear energy or a
fusion
power reactor.
The talk gives an introduction to the LiWF concept for KSTAR
people.
2009, March 17, Renew Workshop Theme 5 -
Optimizing the
Magnetic configuration, PPPL, Princeton
NJ. White paper "ST1,
EAST1,
ITER-100 - all exceeding ignition criterion", and viewgrapths of
the talk as .pdf
file and compact
.pdf2
file.
White paper
summarizes 10 years of LiWF concept, which essentially has
resolved the
plasma physics puzzle of magnetic fusion.
The talk
explains the crucial role of plasma boundary for energy
confinement.
This understanding makes the LiWF regime insensitive to existing
unknowns in transports properties of the plasma core and
essentially
nullifies the value of core transport studies. The appropriate
experiments on NSTX (if modified into ST0 facility for LiWF
regime
studies) can quantify the role of trapped electron modes and
secondary
electron emission and give the necessary data for designing the
next
step spherical tokamak (ST1) for PPPL (capable of demonstrating
DT
ignition relevant plasma parameters using DD plasma), the
stationary
tokamak EAST1 (for fission-fusion studies), and a regime with
100 MW of
DT equivalent fusion power at early (hydrogen) phase of ITER.
2009, January 22,
PPPL Experimental Seminar,
Princeton
NJ, "How far
is
magnetic fusion from being a component of nuclear energy"
.pdf file, and
compact .pdf2
file.
Without abandoning its
noble
goal for clean inexhaustible energy source based on fusion of
hydrogen
isotopes, fusion can much more realistically achieve an
intermediate,
but not less important, goal to be a component of re-emerging
nuclear
energy industry. Instead of producing energy from its 14 MeV
neutrons,
it can better utilize them for converting U-238 or Th-232 into
fissile
elements for the first load of the fast breeder reactors (or
to a
reasonable portion of fuel) in order to close the fuel cycle
of
conventional nuclear reactors.
Three huge problems, i.e., (a)
tritium
breeding in unprecedented amounts, (b) destruction of the
First Wall by
14 MeV neutrons, and (c) extraction of high-temperature
(700-800$^o$ C) heat from the nuclear zone of a toroidal
device, which
are still behind the horizon of "clean" fusion and never been
touched,
are dramatically mitigated to near non-existence in the role
of fusion
as a fuel preparation component of nuclear energy.
Even this "truncated"
fusion-fission
(FF) mission cannot be accomplished based on the present "main
stream"
approach, which as plasma physics research is getting more and
more
fragmented, and is trapped into its hopeless 35 year old
concept of a
fusion power reactor.
Instead, this talk outlines the
theoretical and experimental basis of the LiWall Fusion (LiWF)
concept,
which was first presented to PPPL 10 years ago and which is
based on
new plasma regimes, i.e., "core fueling by neutral beam
injection &
pumping plasma edge by a lithium surface". By eliminating the
dependence of confinement on anomalous electron transport,
edge
localized modes, peaking of the plasma current,
thermo-force
(driving impurities to the plasma), needs for
alpha-particle
heating, etc, LiWF is very well suitable for the FF mission,
suggesting
realistic devices with a JET-size plasma for demonstration of
the FF
mission.
2008, August
25-26, Resonanant Magnetic
Perturbation
Modeling Workshop, General Atomic, San Diego, CA, "Where is
the edge
in toroidal plasmas ?" .pdf file, and
compact .pdf2
file.
It is believed that by
definition the plasma edge is the separatrix which separates
the
confinement zone from the convection dominated plasma
periphery.
Another belief is that the H-mode has a miraculous "edge
transport
barrier" providing a steep temperature pedestal in front of
the last
closed magnetic surface.
The DIII-D experiments with
Resonant
Magnetic Perturbations undermine both of these beliefs. Instead,
the
interpretation of these experiments suggests that the top of the
edge
electron temperature pedestal, rather than the separatrix,
represents the end of the electron energy
confinement
zone, i.e. the edge for the electron temperature. On the
other
hand, the edge for the ion temperature and plasma
density
seems to be situated at the separatrix (or behind it).
The same experiments suggest the
existence of intrinsic MHD perturbations near the separatrix
(probably
related to the Scrape Off Layer Currents measured on DIII-D by
H.~Takahashi) which determine the finite width of the electron
temperature pedestal.
2008, Three talks at
Chinese
Academy of Science, Institute of Plasma Physics, Hefei, Anhui
Province,
China:
1. July 07, 2008,
"The LiWall Fusion
(LiWF)
Concept (part I)" .pdf file, and
compact .pdf2 file.
2. July 09, 2008,
"LiWF
&
Spherical Tokamaks (part II)" .pdf file, and
compact .pdf2
file.
3. July 14, 2008,
"Three
Step
Program toward the Reactor Development Facility (RDF, part
III)" .pdf file, and
compact .pdf2
file.
All critical aspects as
well
as existing theoretical and experimental data which support
the
new approach to magnetic fusion are outlined in three talks in as
systematic manner.
2008, April
15 Experimental Seminar, PPPL,
Princeton NJ, 2008,
March 26, 21st
Transport Task Force
(Boulder CO), "Where
is the edge in toroidal plasmas"
.pdf file, and
compact .pdf2 file.
It is believed that by definition the plasma edge is the
separatrix
which separates the confinement zone from the convection dominated
plasma periphery. Another belief is that the H-mode has a
miraculous
"edge transport barrier" providing a steep temperature pedestal in
front of the last closed magnetic surface.
DIII-D experiments with Resonant Magnetic Perturbations undermine
both of these beliefs. In addition, the recent
discovery of the instability of the so-called Wall Touching
Kink Modes (and their edge version, the Takahashi Kink Modes)
gives a
basis
for an emerging self-consistent understanding of the plasma edge
and
its MHD activity.
2008, March 24, Physics Seminar at University of
Wisconsin
(Madison WI), March 25, University
of Illinois Urbana (Champaign IL), "LiWall
Fusion and its 3 step R&D program toward a Reactor
Development
Facility" .pdf file,
and
compact .pdf2 file.
2008, January 10, Theory
Meeting, PPPL, Princeton NJ, "The kink
mode
during the disruptions" .pdf file
and
compact
, .pdf2
file.
The talk explains the locked m/n=1/1 kink mode during the vertical
disruption event when the plasma has an electrical contact with
the
plasma facing conducting surfaces. It is shown that the kink
perturbation can be in equilibrium state even with a stable safety
factor q > 1, if the halo currents, excited by the kink mode,
can
flow through the conducting structure. This suggests a new
explanation
of the toroidal asymmetry in magnetic measurements and so-called
sideway forces on the in-vessel components
during the disruption event.
In addition, the talk confirms the fundamental role of the halo
currents
(named here as "Hiro" currents), which interaction with the free
boundary kink modes
was in many occasions emphasized earlier by Hiro Takahashi and
Eric
Fredrickson. In fact, the physics of Hiro currents can explain
four edge plasma stability regimes in tokamaks in a way consistent
with
DIII-D experiments.
2007, November 16,
APS-2007 Meeting (Rosen
Center Hotel,
Orlando FL), "The
theory of
the failure of magnetic fusion"
.ps file,
.pdf file
and
compact
.ps2 file,
.pdf2 file.
In the physics of the 20th century, fusion represents an
extraordinary failure which eroded expectations of society
on an
``unexhaustible'' energy source. The question is if these 50 years
of
research did really prove that fusion will be forever a "carrot''
on a
stick and always 35 years from its implementation.
When a person is asking fusion people why this program is full
of
broken promises, he (besides conventional complaints on the lack
of
funding) is typically getting the answer that the problem itself
is the
most difficult one
that
physics ever faced. In the FSU, such characterizations were done
as
early as in the 60s by Lev Artsimovich, the leader in the field.
This view is only partially applicable in the 21st century. Since
the
Artsimovich time, fusion, as a "difficult''
problem, has been converted into the "complicated'' one
(around the late 80s). The presented theory makes a clear
distinction
between these two kinds of problems, which require significantly
different management approaches, and explains the current
stagnation in
magnetic fusion by the lack of understanding this crucial
difference.
The "difficult''
problem self-organizes its own solution and does not require
intervention of management. The state of the "difficult''
problem is improving with time.
If an unresolvable issue was encountered, the "difficult'' problem
is
converted into a "complicated''
one. Without external intervention, the "thermal death'' state of
the "complicated''
problem is getting only worse with time.
There is no natural way back from the "complicated'' phase.
Only an external "brute'' force with "low entropy'' means
(computers,
money, and sufficient intellect to make the problem "difficult''
again) can reverse the situation.
Accordingly, it is not possible to expect that, without changing
the
management approach (or starting a new program), the hopelessly
fragmented magnetic
fusion would be capable to deliver the promised energy
source.
2007, October 24-30, Fusion Energy Seminars in LANL (Los
Alamos
NM), GA (San Diego CA), UCLA (Los Angeles CA),
LLNL (Levermore CA), "LiWall
Fusion and its 3 step R&D program toward a Reactor
Development
Facility"
.ps file,
.pdf file
and
compact .ps2 file,
.pdf2 file.
The talks in several fusion Labs were a response to the
Orbach/Bodman
initiative for domestic fusion. In particular, the proposed
program
includes short term experiments on plasma pumping with a lithium
loaded
plate on NSTX and conversion of this machine into a spherical
tokamak
ST0 with a mission to demonstrate the feasibility of the LiWall
regime
with 2-3 times better confinement than at present on NSTX.
2007, August 07, FESAC Strategic Planning Panel
meeting,
PPPL Princeton NJ, "LiWall
Fusion and its 3 step R&D program" (2 slide
presentation) .ps file,
.pdf file
and White
paper .ps file, .pdf file,
The presentation was made as a response to the FESAC charge by the
Director of the DoE Office of Science R. Orgach on domestic fusion
program beyond the ITER. The essence of the LiWall Fusion
(LiWF)
concept was explained in a compact form together with its R&D
program targeting development of the Reactor Development Facility.
Early this absolutely necessary step in developing a practical
fusion
was known as a neutron source but then abandoned because of
incapability of magnetic fusion to meet the RDF's requirements.
Now,
with LiWF concept completed, the RDF seems to be within present
plasma
physics and technology. In contrast to LiWF, the presently
dominant
concept of fusion, referred as the BBBL-70s ("The Bibble
of
the 70s"), with its "road map" and "burning plasma" projections,
appears to be irrational and non-scientific in all crucial issues
of
fusion as a possible energy source.
2007, April 11, PPPL
Colloquium,
PPPL Princeton NJ, "3-step
program toward a Reactor Development Facility",
.ps2 file
.pdf file
.pdf2 file.
The presently adopted plasma physics concept of magnetic fusion
has originated from the idea of providing low plasma edge
temperature as a condition for plasma-material interaction.
During 30-years of its existence this concept has shown to
be not
only incapable of addressing practical reactor development
needs,
but also to be in conflict with fundamental aspects of
stationary
and stable plasma.
Meanwhile, a demonstration of exceptional pumping capabilities
of
lithium surfaces on T-11M (1998), discovery of the quiescent
H-mode regime on D-IIID (2000), and a 4 time enhancement of
the
energy confinement time in CDX-U tokamak with lithium
(2005),
contributed to a new vision of fusion relying on high edge
plasma
temperature. The new concept, called LiWalls, provides a
scientific basis for developing magnetic fusion.
The talk outlines 3 basics steps toward the Reactor
Development
Facility (RDF) with DT fusion power of 0.3-0.5 GW and a
plasma
volume ~30 m^3. Such an RDF can accomplish three reactor
objectives of magnetic fusion, i.e., (a) high power density
~10
MW/m^3 plasma regime, (b) self-sufficient tritium cycle, (c)
neutron fluence ~10-15 MW⋅ year/m^2, all necessary for
designing
the DT power reactor. Within the same mission a better
assessment
of DD fuel for fusion reactors could also be possible.
The suggested program includes a series of 3 spherical
tokamaks.
Two of them, ST1, ST2, are DD-machines, while the third one,
ST3,
is the RDF itself with a DT plasma and neutron production.
All three devices rely on a NBI maintained plasma regime
with
absorbing wall boundary conditions provided by the Li based
plasma facing components. The goal is to utilize the
possibility
of high edge temperature plasma with the super-critical
ignition
(SGI) regime, when the energy confinement significantly
exceeds
the level necessary for ignition by a-particles.
Specifically, the mission of ST1, with a size slightly larger
than NSTX in PPPL but with a four times larger toroidal
field, is
to achieve the absorbing wall regime with confinement close
to
neo- classical. In particular, the fusion factor QDT-equiv~5
corresponding to conventional ignition criterion has to be
achieve.
The mission of ST2, which is a full scale DD-prototype of the
RDF, is the development of all other plasma physics aspects
of stationary regime with QDT-equiv~40-50.
ST3 is the DT device with QDT~40-50 with sufficient neutron
production to design the nuclear component of a power
reactor.
Still the mission of ST3 contains a significant plasma
physics
component of developing a-particle power and He ash extraction.
As a motivational step (ST0), the suggested program, assumes
a
conversion of the existing NSTX device into a spherical
tokamak
with lithium plasma facing components. The demonstration of
complete depletion of the plasma discharge by lithium
surface
pumping, first shown on T-11M, can be considered as a
well-defined criterion of readiness of the machine for the
new
plasma regime. The final mission of ST0 would be doubling or
tripling the energy confinement time with respect to the
current
NSTX.
2006, December 11, NSTX Physics Meeting, PPPL, Princeton NJ, "Lithium and NSTX".pdf file .pdf2 file. Necessity of
new
plasma regimes on NSTX is emphasized and a specific approach
using a Li loaded plate as an option for Li based plasma facing
component on NSTX is presented as a turning point of
its
program toward fusion development.
2006, November 02, Invited talk to APS 2006,
Philadelphia PA, "Ignited
Spherical Tokamaks as a Reactor Development
Facility",
.ps2 file
.pdf file
.pdf2 file.
The
Lithium
Wall Fusion (LiWF) concept, now completed, is presented and
compared
with the "Mainstream" Magnetic Fusion (MMF) approach. While
LiWF is
self-consistent and relies on existing technology and the
present
understanding of fusion, MMF is in conflict with the
science
recommendations regarding all critical issues of the reactor.
Necessity
of a separate, reactor development program (~$2-2.5B for ~15
years),
is emphasized.
2006, July 21, UKAEA
Fusion
Theory Colloquium, UK,
"Getting
serious
about
Fusion",
.ps2 file
.pdf file
.pdf2
file.
This
provocatively titled talk presents an unconventional view on the
basic
issues of magnetic fusion (excluding its nuclear issues), such as:
core
fueling, confinement, stability, power and He extraction from the
plasma. A super-critical regime is suggested
when
alpha heating is not essential for sustained fusion power
production. An unusual similarity between Spherical Tokamaks and
stellarators is also mentioned.
A separate national program (about $2-2.5 B for 15 years), if
launched,
can
realistically develop an Ignited Spherical Tokamak (IST) as
a
fusion neutron source for reactor R&D in 3 steps (2xDD, 1xDT),
i.e.:
1. A spherical tokamak, targeting achievement of the absorbing
wall
regime with neo-classical confinement in a DD plasma and
Q_{DT-equiv}=1,
2. Full scale DD-prototype of IST for demonstration of all aspects
of a
stationary super-critical regime with Q_{DT-equiv}=50.
3. IST itself with a DT plasma for reactor R&D and
alpha-particle
power extraction studies with Q_{DT}=50.
While being focused on the Reactor Development Device (IST), the
approach
is consistent with the smooth transition to the power production
phase
relying on stellarators, as the power reactors, optimized for the
super-critical
ignition regime.
2006, January 25, PPPL Research Seminar, "Thermodynamics,
science
and
religion in fusion",
.ps2 file
.pdf2 file
The talk
represents an extended version of sections 3-5 of the Jan.11
talk. It explains a unique role of the Spherical Tokamaks for
developing a fusion power reactor. Also the analysis of the
situation
in the fusion program (sent earlier
to OSTP) is presented. It explains why, in the absence of
scientific
leaders, such a complicated scientific program, as fusion,
unavoidably
becomes fragmented and fells into an "activity trap". Instead of
being
exposed, the real problems of fusion are put under the rug, the
calibration to the final goal is avoided and replaced by a
propaganda,
and the otherwise good science in the field fails to produce
progress
toward the power reactor. Being thermodynamically equivalent to a
thermostatic, "thermal death" situation, the present state of
fusion
program is essentially irreversible. In order to utilized the
accumulated intellectual, scientific and technical potential of
fusion
it is much more efficient to initiate a separate program,
targeting
Ignited Spherical Tokamaks for development of the power reactor,
than
trying to reverse natural tendencies or fix the current over aged
program.
2006, January 11, PPPL
Research Seminar, "Ignited
Spherical
Tokamaks for
developing a power reactor",
.ps file
.pdf file
The
talk reports
the completion of the LiWall concept and provides argumentation
for
necessity of a special fusion reactor development program based on
ISTs.
2005, October 27,
JET Task Force D Meeting, "Calibrating JET
for
equilibrium reconstruction", .ps file .pdf file
The
calibration technique for JET tokamak is presented. It targets
elimination of uncertainties in magnetic signals due to the
presence of
the iron core and due to eddy currents in passive
conductors. The correlation matrix between sensors located
outside and inside the vacuum vessel is introduced in order to
determine the parasitic n != 0 perturbation in magnetic fields
generated by the iron core. The time dependent matrix of response
functions is introduced in order to eliminate the n != 0
perturbation
generated by the eddy currents. While both elements can be
determined
using only the calibration shots (without the plasma), they allow
to
pre-process magnetic signals of plasma discharges for further use
in
the equilibrium reconstruction codes. The calibration
technique
is planned to be implemented on JET using the existing experience
with
the similar approach developed for CDX-U tokamaks and with
numerical
code Cbc2e.
2005, October 10,
Int. Workshop on Exp. Performance of KTM Tokamak, Astana,
Kazakhstan, Oct.
10-12,
2005, " Ignited
Spherical
Tokamaks for development of power reactor(.ps2 file, .ps file .pdf file)
After
6.5 years since its first formulation the LiWall approach for
tokamak
fusion has demonstrated its conceptual consistency for both
reactor
development and for low-activated reactor itself. While the
currently
dominant tokamak approach is locked into the single concept of
divertor
based power extraction, particle control and He pumping, which is
incapable to resolve any of fundamental magnetic fusion issues
even at
the plasma physics level, the utilizing the Li Wall
properties
opens the way of resolving the energy confinement, plasma
stability,
power extraction, and Helium exhaust problems in a manner
consistent
with the power reactor physics. Instead of useless for reactor
development philosophy of "burning plasma", externally driven
"component test facility", the approach results in Ignited
Spherical
Tokamaks, capable of high fusion power density regime for
developing
the first wall and the tritium cycle of the future power reactors.
2005,
August
11,
Unanswered (too negligible) old message to OSTP, Nov. 2, 2004, "ITER, fusion
and
the power reactor(.pdf file). The reason of stagnation of
the
current magnetic fusion program (more than 35 years old) is
identified
as a lost of the leadership structure in the middle of 1980s when
magnetic fusion felt short in providing a tokamak design concept
capable of 10-15 MW.year/m^2 in fluence of neutrons, necessary for
development of the reactor components. Then, the conceptual
problem was
hidden under the rug, while the subsequent fragmentation of the
research resulted in the "thermal death" situation, when the
fusion
program became entrapped into details of outdated fusion concepts,
at
the same time, blocking the new developments.
The necessity of a separate (from
the current FES) reactor development program for the US is
emphasized.
(See, also Oct. 2004, Fusion Eng. and
Design.)
2005, July 19.
Simposium
on Integrated Modeling, "At the ground
level
of integrated modeling" (.pdf file).
For
any numerical code the number of possible runs can be apprehended
only if expressed at the logarithmic scale in the form of entropy.
What
really limits the entropy is the intellect of the author and his
understanding of the problem rather than "if()" statements inside
the
code. The computer languages, perfect in handling the
"if()"-like
statements, do not provide the adequate mechanism for expressing
the
author's understanding, thus, leaving the entropy of the code
unlimited
for the unexperienced user. The problem could be addressed only if
the
very basic level of integration is formalized in an "entropy-free"
manner using the computer ("entropy-free") power for its
implementation.
The talk discusses the most rudimentary level of integrated
modeling,
level which cannot be avoided or substituted by the sporadic
patching
the loopholes with OOP, FWEB, etc. In 1996 this understanding
resulted
in the CodeBuilder (Cb) idea which became functional in 1997.
It
provides a formalized mechanism for mutual mapping of "people's
minds"
and virtual structures inside the codes, associated sources, data,
documents, etc. While being created earlier than XML (based
on
somewhat similar ideas), Cb represents a more fundamental
approach for resolving the problems of integrated modelling. The
talk
is illustrated with examples of Cb generated codes (Cbesc, Cbbst)
and
their integration with others (ASTRA).
Oct. 2004, Fusion
Eng.
and Design. 72
(2004) 149-168, "Ignited
Spherical
Tokamaks and Plasma Regimes with LiWalls" (.pdf file)
Basic requirements of the fusion power reactor and its development
are
outlined. The notion of Operational Power Reactor Regime (OPRR) is
introduced explicitly for the first time in order to distinguish
it
from the relatively short ignition phase of the reactor operation.
Development of OPRR is intrinsically linked to two basic
technology
objectives, i.e.,
development of the First Wall (FW) and the Tritium Cycle (TC). The
paper reveals an existing fundamental gap in the reactor
development
path associated with the lack of necessary amounts of tritium for
the
reactor design development. In this regard, low recycling regimes
with
a plasma limited by a lithium wall surface suggest enhanced
stability and energy confinement, both necessary for tokamak
power reactors. These regimes also could make ignition and OPRR
feasible in compact tokamaks. Ignited Spherical Tokamaks (IST),
self-sufficient in the bootstrap current, are introduced as a
necessary
interim step for development OPRR-FW-TC for the power reactors.
Tokamaks
with
Lithium covered walls. Year 2004 (-> top)
2004, January 20,27 "Ignited
Spherical Tokamaks and their place in fusion" (.ps file,
.pdf
file)
Presented to Fusion Theory Colloquia, UKAEA and to JET EFDA
Seminar,
Culham, UK.
Three basic aspects of the reactor physics and technology, i.e.,
Operational Power Reactor Regime (OPRR), development of the First
Wall
(FW), and of self-sustained Tritium Cycle (TC) are discussed in
the
talk.
The notion of OPRR is introduced explicitly in order to
distinguish it
from the relatively short ignition phase of the reactor operation.
In
contrast to ignition, OPRR requires new confinement and stability
regimes with high beta (>8 %) and relatively small confinement
time
(<1.5 sec). Being a challenge for the plasma physics, OPRR
cannot be
developed without use of the fusion power. At the same time, the
physics
and technology of FW and TC cannot be developed without OPRR.
Such a generic link between 3 key elements of the reactor physics
together with consumption of large amount of tritium for their
development, creates a gap on the development path toward the
magnetic
fusion reactor.
In this regard, Ignited Spherical Tokamaks (IST) seem to be the
only
feasible concept for bridging the gap between the present physics
and
future power reactors. The expected green light for the ITER puts
development of IST (from the very basic level) into the agenda as
a
necessary and complimentary to ITER fusion reactor R&D
program.
Tokamaks with Lithium covered walls. Year 2003 (-> top)
2003, April 10 "Low
recycling
ITER operational regime, its fueling, pumping and He
control"
(.ps
file, .pdf
file) Presented to APEX/ALPS Meeting, Grand Canion,
AZ .A
recent theory of island held equilibria in tokamaks explains
existence
of a slow evolution phase in the tokamak core even when the
plasma is
"ideally unstable" with respect to m/n=1/1 internal kink mode.
Consistent with TFTR data, this theory predicts unavoidable
major
disruptions in the reference high performance regimes of ITER
and,
thus, requires their considerable revision. As a result, ITER
tentantively should implement the low recycling plasma regime,
which
would not only eliminate the danger of internal disruptions but
would
significantly enhance the ITER performance and lead to its
ignition.
The Diamagnetic "Hot Dog" (DHD) mechanism for refueling and
controlling
the low-recycling high edge temperature ITER operational regime
is
aoutlined. This mechanism provides control of fusion power
deposition,
density and pressure profiles as well as the helium ash exhaust
froma
the plasma. The DHD pumping (inverse to fueling) provides
transport of hot edge plasma particles to Li coated wall panels
(suggested in this regard for ITER wall design), thus making
divertor
consistent with the high plasma edge temperature. At the same
time, the
DHD pumping directs the He ions into the divertor for their
pumping,
thus, suggesting entirely new ITER divertor functionality.
2003, April 03 "Tokamak
reactors,
their strategy, operational regime, fueling and control"
(.ps
file, .pdf
file)
Presented to PPPL Theory Seminar . The talk outlines
objectives
and ten basic rules of magnetic fusion strategy. The low
recycling
Ignited Spherical Tokamaks (IST) are specified as the magnetic
fusion
devices capable of developing the Operational Power Reactor
Regime
(OPRR), First Wall (FW) and the Tritium Cycle (TC). At present,
only
ISTs are consistent with the reactor relevant high-betas,
stationary
regime (maintained by the bootstrap current and by LiWall
pumping),
high fusion power density and neutron flux. The Diamagnetic "Hot
Dog"
(DHD) mechanism for refueling and controlling the low-recycling,
high
edge temperature OPRR is outlined. DHD fueling is consistent
with
controlling fusion power deposition,density and pressure
profiles as
well as with helium ash exhaust from the plasma of power
reactors. The theory of DHD controlled LiWall IST
essentially
concludes the plasma physics concept of tokamak based DT
magnetic
fusion and emphasizes the growing role of fusion technology.
After 4
years the LiWall-DHD development became a practical theory,
requiring
technology and experimental implementation.
2003, March 21 "Negative
central
current and q_0 < 1 equilibria in tokamaks" (.ps file,
.pdf file)
Submitted
to Phys.Rev.Lett. A solution for toroidal equilibria is given
for the situation with a negative current (j(0) < 0) in the
center
of
the plasma column (with a positive overall current). It includes
(a) a
central core region with simply nested magnetic surfaces nd a
negative
total current, (b) an m=1, n=0 magnetic island with a positive
current
density, and (c) an outer region with the conventional magnetic
surfaces
and positive current density. The same solution, applied
for q(0)
< 1 in tokamaks explains the existence of a stationary phase
between
internal relaxations in tokamaks with both central
pressure below
and above the ideal Bussac limit. The theory gives a
classification of relaxation regimes in tokamaks
(consistent with
observations).
2003, March 14 "Operational
Power
Reactor Regime and Ignited Spherical Tokamaks" (.ps file,
.pdf file)
Presented
to Spring 2003 Plasma Science and Fusion Center Seminar at
MIT. While recently submitted to DoE Really Great 35 year
Development Plan (RG35DP) suggests a new, 2003 version of
the
magnetic "cold fusion without ignition" for the next
35
years, the talk was focused on achieving ignition in tokamaks in
the
nearest future. It was shown that the Operational Power Reactor
Regime
(OPRR) requires a wall-stabilized and low recycling
plasma.
Because of the small size and high beta , spherical
tokamaks are
uniquely suitable for development of OPRR. It was shown
that in
the low recycling regime, spherical tokamaks not only are
capable for
OPRR relevant high-beta, but also are overdriven with the
bootstrap
current, calculated now for the first time using direct
Monte
Carlo particle orbit simulations with the pitch angle
scattering.
The Diamagnetic "Hot Dog" (DHD) mechanism for refueling
high-temperature
low recycling plasma has been reported for the first time. DHD
fueling
has all properties for providing full control of the
fusion
power deposition, density and pressure profiles in the low
recycling
tokamak power reactors. The theory of DHD controled LiWall IST
essentially concludes the plasma physics concept of the tokamak
based
DT
magnetic fusion and now requires a phase of its focused
experimental
and
technology development, contrary to the eclectic RG35DP
"configuration
optimization".
2003, February 12 "OPRR, ignited
CTF and Lithium Tokamak Experiment" (.ps file, .pdf file)
Presented
to LTX Meeting at DoE Office of Fusion Energy Sciences. The
Operational Power Reactor Regime (OPRR) (which is distinct from
the
Ignition phase) is introduced as a major challenge for magnetic
fusion.
The necessity for a low recycling regime and a wall-stabilized
plasma
for OPRR is emphasized. For development of the OPRR, Spherical
Tokamaks
(ST) are uniquely positioned as high-$\gb$ small volume
devices
with good plasma confinement and stability. It is shown that
LiWall ST
devices with a low-recyling plasma and wall stabilization have
the
opportunity for ignited operation in a self-sustained magnetic
configuration driven by the bootstrap current. The use of the ST
in
developing the OPRR would provide a new vision for a Component
Test
Facility (CTF) as a compact (30 m^3) ignited ST (0.5 GW of
fusion
power) with high (5-8 MW/m^2) neutron wall load and maximum (up
to 95
%) use of fusion neutrons for tritium breeding. A compact
Lithium
Tokamak Experiment (LTX) is being proposed to address the basic
plasma
physics and technology issues of the low recycling regime,
controlled
by
a lithium wall surface.
2003, January 06 "Magnetic
DEMO,
CTF fusion reactors and their strategy" (.ps file, .pdf file)
Presented
to NSTX Physics Seminar, PPPL, Princeton, NJ. The basic
strategy for development of the DEMO magnetic fusion reactor is
outlined. The strategy distinguishes the Operational Power
Reactor
Regime (OPRR) and the ignition phase. It emphasizes the unique
role of
Spherical Tokamaks with low recycling, high temperature plasma
edge in
developing OPRR. The strategy envisions 3 stages for plasma
physics and
technology development: (a) DD phase with an objective of
development
of quasy-stationary (bootstrap current driven) high-beta ST
regime; (b)
Component Test Facility (CTF) phase based on ignited ST
with
objectives of development of the power extraction schemes (from
both
plasma and the neutron zone) and of a self-sufficient tritium
cycle;
(c) DEMO electricity production phase, based on
conventional
aspect ratio tokamaks with Li/FLiBe based first wall, full
shielding
and
high-temperature FLiBe coolant and a self-sufficient
tritium
cycle with an objective of demonstration consistency of the
magnetic
fusion with the safety and economics of the power reactor.
Tokamaks with Lithium covered walls. Year 2002 (-> top)
2002, October 30
"Dynamically
balanced
first wall for the LiWall tokamak-reactor" (.ps file, .pdf file)
Presented
to 5th US-Japan Workshop on Fusion High Power Density Devices
and Design, UCLA, Los Angeles, CA. The shape of the dynamically
balanced
first wall has been calculated. The wall structure includes: a) ~1
cm
thick intense plasma facing lithium streams driven by magnetic
propulsion, b) ~1 mm thick patchy separation guide wall, c) Be
wire
ropes balancing the
structure (total maximum thickness of the set ~1 cm), d) ~1 mm
patchy
second separation layer, and e) ~ 10-15 cm
thick Zinkle-Nelson FLiBe blanket. While the existing design
approaches
to the reactor essentially mimic the large plasma experiments and
fail
to satisfy all basic requirements of the reactor physics and cost,
the
presented first wall structure is the first conceptual design
which is
consistent with the high neutron flux, efficient power extraction
as
well as with high performance plasma regimes.
2002, March
08 "Magnetic
propulsion of Intense Lithium Streams in a Tokamak Magnetic
Field" (.ps
file, .pdf file)
Submitted
to Phys. Rev.Letters. The theory of magentic propulsion
(developed in Dec. 1998) is presented for publication.
2002, Feb. 18.
Snowmass 2002 Comments "Li Walls
and
betatau of the fusion reactor strategy". The basic
principles
of magnetic fusion reactor strategy are outlined for further
discussion
(http://web.gat.com/snowmass/working/ci/c2)
2002, Feb.
11,
CEA Cadarache, France , "Tokamak and
tokamak reactors with Li Walls" - (link to .ps and
to .pdf files).
The
LiWall concept has been presented in conjunction with Tore Supra
program on plasma-wall interaction. A section with the
Frequently Asked
Questions has been added to the file.
2002, Feb.
07,
EFDA-JET Seminar, Abingdon UK, "Tokamak
and
tokamak reactors with Li Walls" - (link to .ps and
to .pdf files).
It
was shown that the magnetic fusion has no path without a
substantial
raise in beta. While dominant concept in magnetic
fusion is
full of contradictions, the LiWalls are consistent with basic
reactor
requirements. Being in all plasma physics aspects more advanced
than
the
conventional fusion, LiWalls it is the only concept making
clean
magnetic fusion realistic.
Tokamaks
with
Lithium covered walls. Year 2001 (-> top)
2001, Feb. 26,
Seminar of Dept. of Nuclear Engineering, MIT
, "Yacht-sail
approach
for the tokamak fusion reactors" - (link to .ps and to .pdf files).
Dynamically
balanced design concept for the "first wall" of the tokamak
fusion reactor has been presented to MIT students. The concept
opens
opportunities for creativity of nuclear engineers and
technologists in developing acceptable and controllable
tokamak
fusion reactor.
2001, Feb. 21.
Sergei
Mirnov Talk at PPPL Experiment Seminar, "Experiments
on
Tokamak T-11M with a Lithium Capillary-Pore Limiter" - link to
the
PowerPoint .ppt file. Same viewgraphs (although without
comments)
in JPEG format (e.g.,Mirnov01.jpg) can be accessed
at
http://w3.pppl.gov/~zakharov/Mirnov010221.
2001, Jan. 29, "Stabilization
of
tokamak plasma by lithium streams" - .ps file with
submission to
Comments on Plasma Phys. and Controlled Fusion. A pure
academic
manuscript, which describes a mechanism of MHD stabilization by
Intense
Lithium Streams at the plasma edge, discovered together with the
LiWall
concept in Dec. 1998. Was motivated for publication in summer of
1999
by a misrepresentation of the LiWalls at the Sherwood-1999
Theory
meeting at Los Angeles. Manuscript wasted more than a half year
in PRL.
Slightly different from the PPPL-3483 report.
2001, Jan. 26, OFES
of
DoE, "Tokamaks
with
LiWalls
as a concept for fusion reactor" (.ps file,
identical
to
UMD, but presented with a different emphasis).
2001, Jan.
25,
Theory seminar of Institute for Plasma
Research, University of Maryland, "Tokamaks
with
LiWalls: what is interesting about them" (.ps file,
slightly
different from the PU Ph. Dept. talk on Dec.07, 2000, i.e.,
without
Cbpu code involved).
2001, Jan. 18,
Theory
seminar at PPPL, "TFTR,
DIII-D, and
non-recycling regime in tokamaks" - (.ps file with
a little
bit
of what plasma physicists and students should know about low
recycling regimes in tokamaks.)
Outline of this 90
min
talk:
{
I. Research results in physics.
a) TFTR
(link
to .ppt file of D.Mansfield),
b)T-11M lithium results (link does not yet exist),
c) DIII-D
QDBH
(.pdf link to a copy of K.Burrell, GA, presentation to
APS-2000),
d) Non-recyling
LiWall
(1998) (.ps link to my PU talk, see pp.14-16), and
c) Sakharov's (1951)
regimes.
II. Does the
tokamak
fusion has a path ?
a) Yes.
b) Consistency between DoE
/
Congress
approach to fusion. (link to a US gov. WW2 history document /
Views of
a
Republican Congressman, who can be credited for the shock
therapy for
the tokamak fusion) .
c) Competence in research and
d) Freedom of communications as a key for securuty of our
progress in
fusion.
e) Safety of future reactors (any kind of covering up
the
present reality
from students is 100 \% guarantees of future failures with the
fusion
reactors) .
III. Yes, it has it and soon it will be on the way.
}
2001, Jan. 12.,
PS&T seminar at PPPL, "Power
extraction
from tokamaks and tokamak-reactors" - (link to .ps file).
Abstract, as
it
was announced to PPPL Staff. (Another
version, intentionally falsified by the current PPPL
management, has
been put on PPPL weekly highlights http://www.pppl.gov/hypermail/PPPL_Highlights/0172.html
.)
{
Only two aspests of the LiWall concept will
be
discussed in
presentation :
(a) power extraction
from
the plasma facing components in tokamaks
and
(b) power extraction from the energy absorption layer in the
neutron
zone of the tokamak-reactor, which includes
the a new "Yacht sail"
approach for the tokamak-reactor design,
(other issues will be
discussed on Jan. 18 and on consequitive PPPL
seminars).
For the first time in
the
quasi-stationary fusion, LiWall concept
provides a consistent approach for solving both problems
of
power extraction. It also opens for US fusion program
practically
unlimited
RESEARCH capabilities
(presumably, up
to
ignition and burning plasmas)
on tokamaks with the Li coated copper walls.
The presentation
makes
obvious to broad audience of physicists the
progmatic and scientific meaningless of continuing the
"compact"
stellarator project in PPPL.
}
2001, Jan. 11 "On
new reality in tokamak physics and fusion" ("Necessity (a)
of
initiating LiWall research program and (b) terminating the
"compact"
stellarator project (NCSX)") - (link to .html file
with my
message of Jan.11, 2001 to US fusion leaders and
administraton
and LiW US contributors). LiWalls started their offense for
implementing new reality in the best fusion Lab in the World,
PPPL.
Tokamaks
with
Lithium covered walls. Year 2000 (-> top)
2000,Dec.12,
University
of Texas, Austin, TX, Burning Plasma
Workshop (Boudary physics discussion).
LiWall concept started to trace its research path to
burning
plasma and tokamak-reactor.
"Lithium
Walls as
the Plasma Facing Surface for the tokamak-reactors" -link to
.ps file
(link to
.pdf file).
2000, Dec. 07,
Princeton University, Physics Department
Colloquium. LiWall concept broke the shell of cover up
(created by
PPPL manegment) and started to talk to physicists outside
fusion.
"Tokamak
Fusion,
does it have a path ?" -link to .ps file and .pdf
file
(this .pdf is not a good conversion from .ps) . The file
only
contains what stayed behind
the talk. It contains the most complete presentation of
the
LiWall concept at this moment.
Absract of the PU talk
{
Tokamak fusion devices, which for 3 decades were leaders in the
World
fusion program and which made a leap from 1 keV plasma
temperature in Russian T-3 machine (1968) to 40 keV
and 10.7 MW of DT fusion power in TFTR at PPPL (1994), are now
in an
eventual state of defeat and possible shutdown in the US.
Despite
much
better understanding of the tokamak plasma now, many
fundamental
problems
on the way to the tokamak-reactor remain unresolved even at the
conceptual level. These problems include stability and steady
state
plasma regime control, power extraction from both the plasma
and the
neutron zone, activation and structural integrity of the
machine
under
14 MeV fusion neutron bombardment, maintenance of future
reactors,
etc.
This presentation
describes the physics of a recently (Dec., 1998)
invented method of magnetic propulsion for driving liquid
metal
streams
in the tokamak magnetic field. This effect in combination
with the
idea
of renewable and absorbing walls at the plasma boundary
(which
previously was only a theoretical abstraction) leads to
breaking with the
conventional approach to the tokamak fusion reactor. The
resulting
new
ideas, which in many aspects rely on the best US tokamak
experiments
on TFTR
(PPPL) and DIII-D (GA, San Diego) and basic theory, raise the
hope
on a
new research path for tokamaks toward a practical fusion
reactor.
}
Tokamaks with
lithium
wall - a new way for tokamak fusion and
tokamak science ???
2000, Nov. 13-17,
ALPS/APEX Meeting, Albuquerque, NM, SNL.
(4
talks) :
1. "Power
extraction by liquid metal jets" (link to .ps file)
(link to
.pdf file)
2.
"Stabilization
of tokamak plasma by lithium streams" (link to .ps file)
(link to
.pdf file)
3.
"Zinkle/Nelson Concept of Dual Lithium Stream First Wall/FLiBe
blanket
for tokamak-reactor" (link to .ps file) (link to
.pdf
file)
4.
"Overview of TFTR Li experiments" (link to .ppt file)
(short version of D.Mansfield APS2000 presentation reported to
APEX
meeting by L.E.Zakharov)
2000, Oct.25-26
mini-Conference on Lithium Walls and Low Recycling
Regimes, APS/DPP 2000, Quebec City, Canada,
"Lithium
walls
and Low Recycling Regimes in Tokamaks" - link to
Agenda of 2 day mini-Conference with a number
of
presentation titles linked to presentation files.
2000, May 08, ALPS/APEX Meeting (May 8-12) at Argonne Nat.
Lab.,
Chicago IL, "Intense
Lithium Streams in Tokamaks" link to .ps file
with
presentation to APEX
/ ALPS(ALPS
link may
not
work). Close loop for intense lithium streams in tokamak has
been
analyzed at a basic level. It was shown that lithium streams
provide
necessary power extraction capability for reactor
applications. APEX
, which initially rejected magnetic propulsion at
Snowmass
meeting, finally dropped its idea on liquid FLiBe first
wall in
tokamaks as incompatible with plasma requirements. Also, the
concept of
thick liquid metal walls has been droped as incompatible with
liquid
metal MHD.
2000, May 09,
ALPS/APEX Meeting (MAY 8-12) at Argonne Nat. Lab.,
Chicago IL, "Proposal
on
Lithium Wall Experiment (LWX) on PBX-M" link
to
presentation to on multi-institutional proposal for LiWall
program in
the US. PBX-M tokamak, the only one left in PPPL after
distruction of
TFTR and PLT, has been proposed as a test bed for the program.
Tokamaks
with
Lithium covered walls. Year 1999 (-> top)
1999, Sep. 09, US-Japan woorkshop on "High betas" (Sep. 8-20)
at GA
, San-Diego, CA, "The
prospects for
high-beta tokamaks with Li walls " link to
presentation.
(Essense
of the non-recycling regime in eliminating
thermo-conduction
energy loss explained qualitatively, Numerical
calculations
of pressure limits for this regime was presented).
"Magnetic
propusion
for driving liquid lithium walls" link to
2-page long summary file on magnetic propulsion and associated
issues prepared for 1999 Fusion
Summer
Study workshop in Snowmass "Opportunities
and
Directions in Fusion Energy Science for the Next Decade" .
Was
excluded from final documents of the workshop by the
fusion
"opportunity seekers" disciminating everything, which does not
fit the
established status quo in the fusion program.
"A
tokamak
reactor with lithium walls" link to 2-page
long summary
.ps
file on the concept prepared for 1999 Fusion
Summer Study workshop
in Snowmass "Opportunities and Directions in Fusion Energy
Science for the Next Decade" . Was excluded
from final
documents of the workshop by the fusion "opportunity seekers"
disciminating everything, which does not fit the established
status quo
in the fusion program.
"Magnetic
propulsion of liquid lithium in tokamaks" Link
to
presentation to "IEA Workshop on Liquid Metal R & D for
Fusion
Applications" , Argonne NL IL, April 26, 1999. Not useful
as
repeats previous material. First presentation to technology ALPS (link
may nor
work) people working on Advanced Limiter-divertor Plasma
facing
Surfaces. Collaboration with US technology side has been
established.
"Magnetic
propulsion
of conducting fluid and the theory of controlled tokamak
reactor" link to .ps file with the first
presentation on magnetic propulsion to PPPL on Jan. 08, 99. Link
is
not
useful as it does not contain any pictures. Nevertheless, that
time,
the basic theory of magnetic propulsion has been developed and
the new
concept for tokamaks has been formulated. Also, for the first
time, I
raised clear objections of the administation decision to destroy
TFTR
and other tokamaks in PPPL which could acquire untouched
potential if
modified for lithium wall studies.
Numerical codes and
the
theory. (-> top)
Real
Time
Forecast (RTF) of tokamak discharges. (-> top)
2004, December 09, UKAEA
Theory
Colloquium (Culham, UK), "Equilibrium
reconstruction in eddy current environment in tokamaks"
In middle and small size tokamaks the eddy currents in the passive
structures affect both the interpretation of magnetic signals and
the
plasma equilibrium. Complicated and essentially unpredictable
current
paths of eddies add a considerable problem to equilibrium
reconstruction, one of the widely used tools fortokamak
diagnostics.
The presented theory introduces the response functions of
magnetic signals as a necessary element of magnetic
reconstruction. The appropriate system of equilibrium
reconstruction equations, which uses the time history of the
discharge
and signals, mitigates uncertainties associated with the eddy
currents
and allows for a proper weighting of equations. The theory gives a
guidance for calibrating the magnetic diagnostics in tokamaks for
purposes of equilibrium reconstruction as well as a method of
recovering the response functions from measurements.
2004, December 09,
EFDA-JET Seminar (Culham, UK),
June 4, DIII-D Science Meeting(GA,
CA San diago, CA), June
16,
PPPL
Research Seminar (Princeton, NJ) "On Real Time
Forecasts (RTF) of Tokamak Discharges" (.ps file, .pdf file)
This
talk discusses the possibility to extend the existing experience
with the real time equilibrium reconstruction by linking it with
transport simulations and, thus, to approach the RTF of tokamak
discharges. Unlike transport analysis codes (similar to
"yesterday"
weather analysis) or predictive codes ("next month" weather
predictions), RTF targets a forecast of the plasma regime, e.g.,
in 0.1
tau_E (like the "next hour" weather predictions).
Three components, crucial for RTF are discussed: (a) fast
equilibrium calculations, (b) fast transport calculations for
stiff
models, and (c) computer assisted control of numerical codes and
their
communications, documentation, maintenance and interaction with
other
codes and drivers.
In this regard, (a) a new set of linearized equilibrium equations
have
been derived; (b) a shooting technique for stiff transport models
has been tested and shown to have two orders of magnitude
faster
convergence than the conventional implicit scheme; and (c) the
CodeBuilder software for controlling the codes and communications
was
used for ESC-ASTRA-DCON-BALLLON code system as a RTF prototype.
The
theory
of Equilibrium reconstruction (-> top)
2007, June 6, Russian Conference on High Temperature
Plasma Diagnostics, Zvenigorod, Moscow region, RF,
"EquilibrZven070607.pdfium
reconstruction
of q- and p- profiles in ITER using different external
and internal measurements",
.ps2 file
.pdf file
.pdf2
file.
Based on an earlier presentations (see below), the talk outlines a
theory of variances in the reconstructions of the plasma current
density and pressure profiles in the Grad-Shafranov equation. The
associated technique was incorporated into the ESC code. Potential
variances in q- and p- profiles have been calculated for different
sets
of external and internal measurements envisioned for equilibrium
reconstruction in ITER. It was shown that complementing the
external magnetic measurements with either Stark line polarization
signals (MSE-LP) or with recently proposed for ITER by Nova
Photonics
line shift signals (MSE-LS) can significantly improve the
reliability
of the reconstructed plasma profiles and the magnetic
configuration.
Capabilities of calculating variances, incorporated into the
numerical
code ESC, have completed the theory of reconstruction, which for a
long
time had a significant gap in ability to evaluate the
quality of
the presently widely used equilibrium reconstruction technique.
2007, April 20, Science Meeting, General Atomic, San
Diego
CA,
"Consideration
of
variances in
equilibrium reconstruction", .pdf
file.
With small modications same as 2007,
March 20 talk (see below)
to PPPL
Experimental Seminar, Princeton NJ.
2007, March 20, PPPL Experimental Seminar, Princeton
NJ,
"The
theory
of equilibrium
reconstruction and a possibility of complete reconstruction in
ITER",
.ps2 file
.pdf file
.pdf2
file.
Potential variances in q- and p- profiles have been calculated for
different sets of external and internal measurements envisioned
for
equilibrium reconstruction in ITER. It was shown that
complementing the
external magnetic measurements with either Stark line polarization
signals (MSE-LP) or with recently proposed for ITER by Nova
Photonics
line shift signals (MSE-LS) can significantly improve reliability
of
reconstruction of plasma profiles and magnetic configuration.
Capabilities of calculating variances, incorporated into numerical
code
ESC, have completed the theory of reconstruction, which for a long
time had a significant gap in ability to evaluate the
quality of
the presently widely used at present equilibrium
reconstruction
technique.
2006,
August
08, PPPL
Experimental Research Seminar,
Princeton NJ, "The
theory of variances of
equilibrium current density reconstruction",
.ps2 file
.pdf file
.pdf2
file.
Same as
the next on the page talk to EFDA-JET (with some corrections in
calculations).
2006, July 28,
EFDA-JET
seminar, Culham Science Centre,
Abingdon UK,
"The
theory
of variances of
equilibrium current density reconstruction",
.ps2 file
.pdf file
.pdf2 file.
The talk presents a rigorous theory of uncertainties in the
reconstructions of the plasma current density and pressure
profiles in
the Grad-Shafranov equation. The associated technique was
incorporated
into the ESC code, which provides the calculations of
characteristic
cases with different plasma cross-sections, aspect ratios and
current
distributions.
Equilibrium
and
associated codes for download
(-> top)
2007,
"Bishop-Taylor equlibria for
calibration equilibrium and equilibrium reconstruction codes"
Feb 08, 2007
bsh.tgz
-
Cbbsh code for
calculation of the Bishop-Taylor equilibria (with the
C-source and documentation).
Feb 08, 2007
tgz2bsh -
script
generating Cbbsh.
March
01,
2005 esc.tgz - Equilibrium and Stability Code (ESC)
March 01, 2005 tgz2esc -
script
generating Cbesc
(the
CodeBuilder version of ESC)
2004,
"Equilibrium
Spline Interface (ESI) for magnetic confinement codes".
2002, "System
of
compact notations for numerical codes" ( .ps
, .pdf
)
L.E.Zakharov, A.Pletzer, S. Galkin, A.S.Kukushkin.
A rigorous Name Generating System (NGS)
of compact notations for math variables has been developed
for
both case sensitive (e.g., C) and case insensitive (e.g., FORTRAN)
computer codes.
NGS-code (
ngs.Alpha,ngs.Sun,
ngs.LinuxRH,
ngs.c,
(compile
with cc -o ngs
ngs.c))- name
interpretation source
code supplements the system. It accepts the computer name
from
the keyboard, converts it into Latex format and displays the
math
interpretation of the name in an Xdvi window. Download the
appropriate version of the code, set an executable mode to its
file and
type the name of the executable.
Leonid Zakharov (zakharov@pppl.gov)