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Helically Symmetric Experiment

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Title: Helically Symmetric Experiment  
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Subject: Stellarator, University of Wisconsin–Madison, Pegasus Toroidal Experiment, Plasma physics, ADITYA (tokamak)
Collection: Plasma Physics, Stellarators, University of Wisconsin–madison
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Helically Symmetric Experiment

The Helically Symmetric Experiment, abbreviated HSX, stylized as Helically Symmetric eXperiment, is an experimental plasma confinement device at the University of Wisconsin-Madison, which design principles are hoped to be incorporated into a fusion reactor. The HSX is a modular coil stellarator which is a toroidal shaped pressure vessel with external electromagnets which generate a magnetic field for the purpose of containing a plasma.

Contents

  • Background 1
  • Device 2
  • Subsystems, diagnostics 3
  • Goals and major achievements 4
  • Ongoing experiments 5
  • See also 6
  • References 7
    • Additional resources 7.1
  • External links 8

Background

A stellarator is a magnetic confinement fusion device which generates all required magnetic fields to confine high temperature plasma by external magnetic coils. Unlike in tokamaks and reversed field pinches, no toroidal plasma current is required in stellarators to confine the plasma. Lack of this large externally driven plasma currents makes stellarators suitable for steady-state fusion power plant. However, due to non-axisymmetric nature, conventional stellarators have a combination of toroidal and helical modulation of the magnetic field on a magnetic field line that leads to high transport of plasma out of the confinement volume at fusion relevant conditions. This large transport in conventional stellarators can limit their performance as a fusion reactor. This problem can be largely reduced by tailoring the magnetic field geometry. The dramatic improvements in computer modeling capability in the last two decades has helped to "optimize" the magnetic geometry to reduce this transport resulting to a new class of stellarators called "quasi-symmetric stellarators". Computer-modeled odd-looking electromagnets will directly produce the needed magnetic field configuration. These devices combine good confinement properties of tokamaks and steady-state nature of conventional stellarators. The Helically Symmetric Experiment (HSX) at the University of Wisconsin-Madison is a quasi-helically symmetric stellarator (helical axis of symmetry). HSX is the first and only operating quasi-symmetric stellarator in the world and will continue to have this distinction until Wendelstein 7-X stellarator, currently being built in Germany, is operating.

Device

The magnetic field in HSX is generated by a set of 48 twisted coils arranged in four field periods. HSX typically operates at a magnetic field of 1 Tesla at the center of the plasma column. A set of auxiliary coils is used to deliberately break the symmetry to mimic conventional stellarator properties for comparison. HSX vacuum vessel is made of stainless steel, and is helically shaped to follow the magnetic geometry. Plasma formation and heating is achieved using 28 GHz, 100 kW electron cyclotron resonance heating (ECRH). A second 100 kW gyrotron has recently been installed on HSX to perform heat pulse modulation studies. Plasmas as high as 3 kilo electronvolts in temperature and about 8x10^12/cc in density are routinely formed for various experiments.

Subsystems, diagnostics

HSX has a large set of diagnostics to measure properties of plasma and magnetic fields. The following gives a list of major diagnostics and subsystems.

Goals and major achievements

HSX has made and continues to make fundamental contributions to the physics of quasisymmetric stellarators that show significant improvement over the conventional stellarator concept. These include:

  • Measuring large ion flows in the direction of quasisymmetry
  • Reduced flow damping in the direction of quasisymmetry
  • Reduced passing particle deviation from a flux surface
  • Reduced direct loss orbits
  • Reduced neoclassical transport
  • Reduced equilibrium parallel currents because of the high effective transform

Ongoing experiments

A large number of experimental and computational research works are being done in HSX by students, staff and faculties. Some of them are in collaboration with other universities and national laboratories, both in the USA and abroad. Major research projects at present are listed below:

  • Effect of quasi-symmetry on plasma flows
  • Impurity transport
  • Radio frequency heating
  • Supersonic plasma fueling and the neutral population
  • Heat pulse propagation experiments to study thermal transport
  • Interaction of turbulence and flows in HSX and the effects of quasi-symmetry on the determination of the radial electric field
  • Equilibrium reconstruction of the plasma density, pressure and current profiles
  • Effects of viscosity and symmetry on the determination of the flows and the radial electric field
  • Divertor flows, particle edge fluxes
  • Effect of radial electric field on the bootstrap current
  • Effect of quasi-symmetry on fast ion confinement

See also

References


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local libraryUtil = require('libraryUtil') local checkType = libraryUtil.checkType local mArguments -- lazily initialise Module:Arguments local yesno -- lazily initialise Module:Yesno

local p = {}


-- Helper functions


local function getArgs(frame) -- Fetches the arguments from the parent frame. Whitespace is trimmed and -- blanks are removed. mArguments = require('Module:Arguments') return mArguments.getArgs(frame, {parentOnly = true}) end

local function removeInitialColon(s) -- Removes the initial colon from a string, if present. return s:match('^:?(.*)') end

function p.findNamespaceId(link, removeColon) -- Finds the namespace id (namespace number) of a link or a pagename. This -- function will not work if the link is enclosed in double brackets. Colons -- are trimmed from the start of the link by default. To skip colon -- trimming, set the removeColon parameter to true. checkType('findNamespaceId', 1, link, 'string') checkType('findNamespaceId', 2, removeColon, 'boolean', true) if removeColon ~= false then link = removeInitialColon(link) end local namespace = link:match('^(.-):') if namespace then local nsTable = mw.site.namespaces[namespace] if nsTable then return nsTable.id end end return 0 end

function p.formatPages(...) -- Formats a list of pages using formatLink and returns it as an array. Nil -- values are not allowed. local pages = {...} local ret = {} for i, page in ipairs(pages) do ret[i] = p._formatLink(page) end return ret end

function p.formatPageTables(...) -- Takes a list of page/display tables and returns it as a list of -- formatted links. Nil values are not allowed. local pages = {...} local links = {} for i, t in ipairs(pages) do checkType('formatPageTables', i, t, 'table') local link = t[1] local display = t[2] links[i] = p._formatLink(link, display) end return links end

function p.makeWikitextError(msg, helpLink, addTrackingCategory) -- Formats an error message to be returned to wikitext. If -- addTrackingCategory is not false after being returned from -- Module:Yesno, and if we are not on a talk page, a tracking category -- is added. checkType('makeWikitextError', 1, msg, 'string') checkType('makeWikitextError', 2, helpLink, 'string', true) yesno = require('Module:Yesno') local title = mw.title.getCurrentTitle() -- Make the help link text. local helpText if helpLink then helpText = ' (help)' else helpText = end -- Make the category text. local category if not title.isTalkPage and yesno(addTrackingCategory) ~= false then category = 'Hatnote templates with errors' category = string.format( '%s:%s', mw.site.namespaces[14].name, category ) else category = end return string.format( '%s', msg, helpText, category ) end


-- Format link -- -- Makes a wikilink from the given link and display values. Links are escaped -- with colons if necessary, and links to sections are detected and displayed -- with " § " as a separator rather than the standard MediaWiki "#". Used in -- the template.


function p.formatLink(frame) local args = getArgs(frame) local link = args[1] local display = args[2] if not link then return p.makeWikitextError( 'no link specified', 'Template:Format hatnote link#Errors', args.category ) end return p._formatLink(link, display) end

function p._formatLink(link, display) -- Find whether we need to use the colon trick or not. We need to use the -- colon trick for categories and files, as otherwise category links -- categorise the page and file links display the file. checkType('_formatLink', 1, link, 'string') checkType('_formatLink', 2, display, 'string', true) link = removeInitialColon(link) local namespace = p.findNamespaceId(link, false) local colon if namespace == 6 or namespace == 14 then colon = ':' else colon = end -- Find whether a faux display value has been added with the | magic -- word. if not display then local prePipe, postPipe = link:match('^(.-)|(.*)$') link = prePipe or link display = postPipe end -- Find the display value. if not display then local page, section = link:match('^(.-)#(.*)$') if page then display = page .. ' § ' .. section end end -- Assemble the link. if display then return string.format('%s', colon, link, display) else return string.format('%s%s', colon, link) end end


-- Hatnote -- -- Produces standard hatnote text. Implements the template.


function p.hatnote(frame) local args = getArgs(frame) local s = args[1] local options = {} if not s then return p.makeWikitextError( 'no text specified', 'Template:Hatnote#Errors', args.category ) end options.extraclasses = args.extraclasses options.selfref = args.selfref return p._hatnote(s, options) end

function p._hatnote(s, options) checkType('_hatnote', 1, s, 'string') checkType('_hatnote', 2, options, 'table', true) local classes = {'hatnote'} local extraclasses = options.extraclasses local selfref = options.selfref if type(extraclasses) == 'string' then classes[#classes + 1] = extraclasses end if selfref then classes[#classes + 1] = 'selfref' end return string.format( '
%s
', table.concat(classes, ' '), s )

end

return p-------------------------------------------------------------------------------- -- Module:Hatnote -- -- -- -- This module produces hatnote links and links to related articles. It -- -- implements the and meta-templates and includes -- -- helper functions for other Lua hatnote modules. --


local libraryUtil = require('libraryUtil') local checkType = libraryUtil.checkType local mArguments -- lazily initialise Module:Arguments local yesno -- lazily initialise Module:Yesno

local p = {}


-- Helper functions


local function getArgs(frame) -- Fetches the arguments from the parent frame. Whitespace is trimmed and -- blanks are removed. mArguments = require('Module:Arguments') return mArguments.getArgs(frame, {parentOnly = true}) end

local function removeInitialColon(s) -- Removes the initial colon from a string, if present. return s:match('^:?(.*)') end

function p.findNamespaceId(link, removeColon) -- Finds the namespace id (namespace number) of a link or a pagename. This -- function will not work if the link is enclosed in double brackets. Colons -- are trimmed from the start of the link by default. To skip colon -- trimming, set the removeColon parameter to true. checkType('findNamespaceId', 1, link, 'string') checkType('findNamespaceId', 2, removeColon, 'boolean', true) if removeColon ~= false then link = removeInitialColon(link) end local namespace = link:match('^(.-):') if namespace then local nsTable = mw.site.namespaces[namespace] if nsTable then return nsTable.id end end return 0 end

function p.formatPages(...) -- Formats a list of pages using formatLink and returns it as an array. Nil -- values are not allowed. local pages = {...} local ret = {} for i, page in ipairs(pages) do ret[i] = p._formatLink(page) end return ret end

function p.formatPageTables(...) -- Takes a list of page/display tables and returns it as a list of -- formatted links. Nil values are not allowed. local pages = {...} local links = {} for i, t in ipairs(pages) do checkType('formatPageTables', i, t, 'table') local link = t[1] local display = t[2] links[i] = p._formatLink(link, display) end return links end

function p.makeWikitextError(msg, helpLink, addTrackingCategory) -- Formats an error message to be returned to wikitext. If -- addTrackingCategory is not false after being returned from -- Module:Yesno, and if we are not on a talk page, a tracking category -- is added. checkType('makeWikitextError', 1, msg, 'string') checkType('makeWikitextError', 2, helpLink, 'string', true) yesno = require('Module:Yesno') local title = mw.title.getCurrentTitle() -- Make the help link text. local helpText if helpLink then helpText = ' (help)' else helpText = end -- Make the category text. local category if not title.isTalkPage and yesno(addTrackingCategory) ~= false then category = 'Hatnote templates with errors' category = string.format( '%s:%s', mw.site.namespaces[14].name, category ) else category = end return string.format( '%s', msg, helpText, category ) end


-- Format link -- -- Makes a wikilink from the given link and display values. Links are escaped -- with colons if necessary, and links to sections are detected and displayed -- with " § " as a separator rather than the standard MediaWiki "#". Used in -- the template.


function p.formatLink(frame) local args = getArgs(frame) local link = args[1] local display = args[2] if not link then return p.makeWikitextError( 'no link specified', 'Template:Format hatnote link#Errors', args.category ) end return p._formatLink(link, display) end

function p._formatLink(link, display) -- Find whether we need to use the colon trick or not. We need to use the -- colon trick for categories and files, as otherwise category links -- categorise the page and file links display the file. checkType('_formatLink', 1, link, 'string') checkType('_formatLink', 2, display, 'string', true) link = removeInitialColon(link) local namespace = p.findNamespaceId(link, false) local colon if namespace == 6 or namespace == 14 then colon = ':' else colon = end -- Find whether a faux display value has been added with the | magic -- word. if not display then local prePipe, postPipe = link:match('^(.-)|(.*)$') link = prePipe or link display = postPipe end -- Find the display value. if not display then local page, section = link:match('^(.-)#(.*)$') if page then display = page .. ' § ' .. section end end -- Assemble the link. if display then return string.format('%s', colon, link, display) else return string.format('%s%s', colon, link) end end


-- Hatnote -- -- Produces standard hatnote text. Implements the template.


function p.hatnote(frame) local args = getArgs(frame) local s = args[1] local options = {} if not s then return p.makeWikitextError( 'no text specified', 'Template:Hatnote#Errors', args.category ) end options.extraclasses = args.extraclasses options.selfref = args.selfref return p._hatnote(s, options) end

function p._hatnote(s, options) checkType('_hatnote', 1, s, 'string') checkType('_hatnote', 2, options, 'table', true) local classes = {'hatnote'} local extraclasses = options.extraclasses local selfref = options.selfref if type(extraclasses) == 'string' then classes[#classes + 1] = extraclasses end if selfref then classes[#classes + 1] = 'selfref' end return string.format( '
%s
', table.concat(classes, ' '), s )

end

return p

Additional resources

External links

  • Official website


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