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== Comparison of Tokamaks and Stellarators ==

The following table presents a comparative overview of [[tokamak]] and [[stellarator]], based primarily on results and discussions from <ref name="Xu2016" />, together with additional standard literature in magnetic confinement fusion. The comparison highlights key physical properties, transport characteristics, stability behavior, and reactor-relevant challenges of both concepts. The aim is to provide a simplified and coherent picture of the main technical and physical challenges faced by each configuration, and to show how far current experiments are from a practical fusion reactor. <ref name="Xu2016" /><ref name="Spitzer1958" /><ref name="Helander2012" /><ref name="Connor1977" /><ref name="Stroth1998" /><ref name="Xu2013" /><ref name="Stix1973" /><ref name="Helander2007" /><ref name="Feng2011" />

{| class="wikitable sortable"
|+ Comparison between [[Tokamak]] and [[Stellarator]] plasmas
! Aspect
! [[Tokamak]]
! [[Stellarator]]

|-
! colspan="3" style="text-align:center;" | '''Magnetic Geometry and Plasma Confinement'''

|-
| Magnetic field generation
| External toroidal coils + poloidal field from plasma current<ref name="Xu2016" />
| Entirely by external non-axisymmetric (helical) coils<ref name="Xu2016" />

|-
| Axisymmetry
| Axisymmetric configuration<ref name="Xu2016" />
| Non-axisymmetric (three-dimensional)<ref name="Xu2016" />

|-
| Plasma volume
| Typically large
| Usually small

|-
| Aspect ratio (R/a)
| Typically small: 2.5–4
| Usually large: 5–12

|-
| Plasma confinement
| High confinement due to helical field lines; prone to instabilities
| Slightly lower confinement; more stable without plasma current

|-
| Rotational transform
| Mainly from plasma current<ref name="Spitzer1958" /><ref name="Xu2016" />
| From 3D magnetic shaping<ref name="Spitzer1958" /><ref name="Xu2016" />

|-
! colspan="3" style="text-align:center;" | '''MHD stability and operational limits'''

|-
| MHD instabilities
| Many types due to large plasma current
| Very few, mostly small tearing modes

|-
| Plasma current (<math>I_p</math>)
| Large toroidal plasma current required<ref name="Xu2016" />
| No net toroidal plasma current required<ref name="Xu2016" /><ref name="Helander2012" />

|-
| Plasma disruptions
| Major disruptions possible<ref name="Xu2016" />
| Nearly disruption-free<ref name="Xu2016" />

|-
| Beta limit (<math>\beta</math>)
| Limited by ideal-MHD ballooning modes<ref name="Connor1977" /><ref name="Xu2016" />
| Softer beta limit<ref name="Xu2016" />

|-
! colspan="3" style="text-align:center;" | '''Transport and confinement'''

|-
| Diffusivity regimes
| 3 main regimes: neoclassical, Bohm, turbulent
| 4–5 regimes: Classical, neoclassical, turbulent, longitudinal, convective

|-
| Neoclassical transport
| Generally low<ref name="Xu2016" />
| Higher<ref name="Helander2012" /><ref name="Xu2016" />

|-
| Turbulent transport
| Comparable to stellarators<ref name="Stroth1998" /><ref name="Xu2016" />
| Comparable to tokamaks<ref name="Xu2016" />

|-
| ITG (Ion Temperature Gradient) modes
| Collisionless microturbulence; similar behavior in both devices
| Collisionless microturbulence; similar behavior in both devices

|-
| TEM (Trapped Electron Mode)
| Generally unstable; strong electron transport
| Often stabilized by 3D magnetic geometry

|-
| KBM (Kinetic Ballooning Mode)
| High growth at high beta
| Growth reduced; 3D geometry provides partial stabilization

|-
| Pressure gradient (<math>\nabla p</math>)
| Can be large; may drive strong MHD instabilities
| Weaker effect; 3D geometry stabilizes gradients

|-
| Isotope effect
| Clearly observed<ref name="Xu2013" /><ref name="Xu2016" />
| Not clearly observed<ref name="Xu2016" />

|-
! colspan="3" style="text-align:center;" | '''Plasma rotation'''

|-
| Plasma rotation
| Strong toroidal rotation<ref name="Stix1973" /><ref name="Xu2016" />
| Weaker rotation<ref name="Helander2007" /><ref name="Xu2016" />

|-
| Zonal flows
| Weaker damping<ref name="Xu2016" />
| Stronger damping<ref name="Xu2016" />

|-
! colspan="3" style="text-align:center;" | '''Edge and divertor physics'''

|-
| Divertor concept
| Single-null or double-null divertors<ref name="Feng2011" /><ref name="Xu2016" />
| Island or helical divertors<ref name="Feng2011" /><ref name="Xu2016" />

|-
| Impurity control
| Ion-temperature-gradient force often dominant<ref name="Feng2011" /><ref name="Xu2016" />
| Stronger impurity retention<ref name="Feng2011" /><ref name="Xu2016" />

|-
| X-point
| Common; used in divertor to remove heat and impurities
| Less common; 3D geometry often provides natural edge shaping

|-
! colspan="3" style="text-align:center;" | '''Reactor and engineering considerations'''

|-
| Engineering complexity
| Relatively simpler magnetic geometry<ref name="Xu2016" />
| Highly complex coil geometry<ref name="Xu2016" />

|-
| Reactor prospects
| Clear near-term path but challenged by steady-state operation and disruptions<ref name="Xu2016" />
| Attractive long-term option due to steady-state and disruption-free operation<ref name="Xu2016" />

|-
| Next fusion reactor
| DEMO (DEMonstration power plant)
| HELIAS (HELIcal Advanced Stellarator)

|-
| Reactor challenges

|
* Overcome divertor heat load
* Handle high-energy neutron bombardment
* Tritium breeding blanket
* Confine alpha particles at high pressure
* Control instabilities driven by alpha particles

|
* Reduce divertor/edge heat load
* Handle high-energy neutron bombardment
* Tritium breeding blanket
* Confine alpha particles at high pressure
* Limit impact of instabilities and ripple-driven losses
|}

== References ==
<references>
<ref name="Xu2016">Y. Xu, "A general comparison between tokamak and stellarator plasmas", ''Matter and Radiation at Extremes'' '''1''' (2016) 192–200.</ref>
<ref name="Spitzer1958">L. Spitzer, "The stellarator concept", ''Physics of Fluids'' '''1''' (1958) 253.</ref>
<ref name="Helander2012">P. Helander et al., ''Plasma Physics and Controlled Fusion'' '''54''' (2012) 124009.</ref>
<ref name="Connor1977">J.W. Connor and J.B. Taylor, ''Nuclear Fusion'' '''17''' (1977) 1047.</ref>
<ref name="Stroth1998">U. Stroth, ''Plasma Physics and Controlled Fusion'' '''40''' (1998) 9.</ref>
<ref name="Xu2013">Y. Xu et al., ''Physical Review Letters'' '''110''' (2013) 265005.</ref>
<ref name="Stix1973">T.H. Stix, ''Physics of Fluids'' '''16''' (1973) 1260.</ref>
<ref name="Helander2007">P. Helander, ''Physics of Plasmas'' '''14''' (2007) 104501.</ref>
<ref name="Feng2011">Y. Feng et al., ''Plasma Physics and Controlled Fusion'' '''53''' (2011) 024009.</ref>

</references>

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