Helical field stabilization of plasma devices

A toroidal plasma device comprising

• a toroidal confinement vessel for defining a toroidal space and confining gas therein,
• means for generating magnetic flux linking said toroidal space to induce substantial toroidal plasma current therein, said toroidal plasma current producing a substantial poloidal magnetic field,
• first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around the minor circumference of said vessel, and
• means for passing first direct current through said first windings and passing second direct current through said second windings in the direction counter to said first direct current to generate a helical magnetic field acting in combination with said poloidal magnetic field to produce a variation in a safety factor q with minor radius at any poloidal angle whereby the polarity of q reverses near the outer edge of the plasma current, q being defined as the average over a flux surface of the number of transits made around said toroidal space in the toroidal direction by a magnetic flux line in making a single transit in the poloidal direction, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of toroidal magnetic field to poloidal magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU43## where b is a measure of the strength of the magnetic field from said helical windings, R is the major radius of said toroidal space, r is the average minor radius of the magnetic flux surface, B.sub..theta.,o is the poloidal magnetic field produced by said toroidal plasma current, ##EQU44## is the partial derivative of B.sub..theta.,o with respect to r,l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of I.sub.l (kr) with respect to its argument, and q being less than 1 within said plasma current.

A toroidal plasma device comprising

• a toroidal confinement vessel having walls for defining a toroidal space and confining gas therein,
• means for generating magnetic flux linking said toroidal space to induce substantial toroidal plasma current therein, said toroidal plasma current producing a substantial poloidal magnetic field,
• means for generating a vertical magnetic field within said toroidal space, said vertical field being perpendicular to the equatorial plane of said toroidal space,
• first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around the minor circumference of said vessel, and
• means for passing first direct current through said first windings and second direct current through said second windings in the direction counter to said first direct current to generate a helical magnetic field acting in combination with said poloidal magnetic field and said vertical field to produce closed and nested magnetic flux surfaces spaced from said vessel walls, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of toroidal magnetic field to poloidal magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU45## where b is a measure of the strength of the magnetic field from said helical windings, R is the major radius of said toroidal space, r is the average minor radius of the magnetic flux surface, B.sub..theta.,o is the poloidal magnetic field produced by said toroidal plasma current, ##EQU46## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of Il(kr) with respect to its argument, q being defined as the average over a flux surface of the number of transits made around said toroidal space in the toroidal direction by a magnetic flux line in making a single transit in the poloidal direction, and the absolute magnitude of q being less than 1 within said plasma current.

A plasma device comprising

• a confinement vessel having an axis and an axial direction and walls surrounding the axis thereof for defining a space and confining gas therein,
• means for producing substantial plasma current within said space in said axial direction, said plasma current producing a substantial magnetic field around said axis within the plasma,
• first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around said axis, and
• means for passing first direct current through said first windings and second direct current through said second windings in the direction counter to said first direct current to generate a helical magnetic field acting in combination with the magnetic field produced by said plasma current to produce nested magnetic flux surfaces within said plasma, which surfaces are spaced from said vessel walls and are closed in the direction transverse of the axis, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of axial magnetic field to circumaxial magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU47## where b is a measure of the strength of the magnetic field from said helical windings, L is the length of said plasma current within said space, r is the average radius of the magnetic flux surface, B.sub..theta.,o is the circumaxial magnetic field produced by said axial plasma current, ##EQU48## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of I.sub.l (kr) with respect to its argument, q being defined as the average over a flux surface of the number of transits of the length of the plasma current by a magnetic flux line in making a single transit around the plasma current, and the absolute magnitude of q being less than 1 said plasma current.

A plasma device comprising

• a confinement vessel for defining a space having an axis and an axial direction and confining gas therein,
• means for producing substantial plasma current within said space in said axial direction, said plasma current producing a substantial magnetic field around said axis,
• first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around said vessel, and
• means for passing first direct current through said first windings and second direct current through said second windings in the direction counter to said first direct current to generate a helical magnetic field acting in combination with said magnetic field produced by said plasma current to produce a variation in a safety factor q with distance from the center of said plasma current in any direction transverse to said plasma current whereby the polarity of q reverses near the boundary of said plasma current, q being defined as the average over a flux surface of the number of transits of the length of the plasma current by a magnetic flux line in making a single transit around the plasma current, wherein the safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of axial magnetic field to circumaxial magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU49## where b is a measure of the strength of the magnetic field from said helical windings, L is the length of said plasma current within said space, r is the average minor radius of the magnetic flux surface, B.sub..theta.,o is the circumaxial magnetic field produced by said axial plasma current, ##EQU50## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of I.sub.l (kr) with respect to its argument, and the absolute magnitude of q being less than 1 within said plasma current.

A method of operating a toroidal plasma device having a toroidal confinement vessel with walls defining a toroidal space and confining gas therein, said method comprising

• inducing substantial toroidal plasma current in said toroidal space, said toroidal plasma current producing a substantial poloidal magnetic field, and
• generating a helical magnetic field by passing first and second direct currents through respective first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around the minor circumference of said vessel, said second direct current being passed in the direction counter to said first direct current,
• said helical magnetic field combining with said poloidal magnetic field to produce closed and nested magnetic flux surfaces spaced from said vessel walls, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of toroidal magnetic field to poloidal magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU51## where b is a measure of the strength of the magnetic field from the helical windings, R is the major radius of said toroidal space, r is the average minor radius of the magnetic flux surface, B.sub..theta.,o is the poloidal magnetic field produced by said toroidal plasma current, ##EQU52## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of I.sub.l (kr) with respect to its argument, q being defined as the average over a flux surface of the number of transits made around said toroidal space in the toroidal direction by a magnetic flux line in making a single transit in the poloidal direction, and the absolute magnitude of q being less than 1 within said plasma current.

A method of operating a toroidal plasma device having a toroidal confinement vessel with walls defining a toroidal space and confining gas therein, said method comprising

• inducing substantial plasma current in said toroidal space, said toroidal plasma current producing a substantial poloidal magnetic field,
• generating a vertical magnetic field within said toroidal space, said vertical field being perpendicular to the equatorial plane of said toroidal space, and
• generating a helical magnetic field by passing first and second direct currents through respective first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around the minor circumference of said vessel, said second direct current being passed in the direction counter to said first direct current,
• said helical magnetic field combining with said poloidal magnetic field and said vertical field to produce closed and nested magnetic flux surfaces spaced from vessel walls, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of toroidal magnetic field to poloidal magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU53## where b is a measure of the strength of the magnetic field from the helical windings, R is the major radius of said toroidal space, r is the average minor radius of the magnetic flux surface, B.sub..theta.,o is the poloidal magnetic field produced by said toroidal plasma current, ##EQU54## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wavenumber of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l '(kr) is the derivative of I.sub.l (kr) with respect to its argument, q being defined as the average over a flux surface of the number of transits made around said toroidal space in the toroidal direction by a magnetic flux line in making a single transit in the poloidal direction, and the absolute magnitude of q being less than 1 within said plasma current.

A method of operating a plasma device having a confinement vessel with an axis and an axial direction with walls surrounding the axis thereof for defining a space and confining gas therein, said method comprising

• producing substantial plasma current in said space in said axial direction, said plasma current producing a substantial magnetic field around said axis, and
• generating a helical magnetic field by passing first and second direct currents through respective first and second windings wound substantially helically around said vessel with the same sense of twist at substantially the same pitch, said first windings and said second windings being disposed alternately and substantially equally spaced around said axis, said second direct current being passed in the direction counter to said first direct current,
• said helical magnetic field combining with said magnetic field produced by said plasma current to produce nested magnetic flux surfaces within said space, which surfaces are spaced from said vessel walls and are closed in the direction transverse of the axis, wherein a safety factor q within said plasma current is the sum of two components, one being axisymmetric and substantially proportional to the ratio of axial magnetic field to circumaxial magnetic field, and the other being nonaxisymmetric and substantially helically symmetric and substantially the quantity ##EQU55## where b is a measure of the strength of the magnetic field from said helical windings, L is the length of said plasma current within said space, r is the average radius of the magnetic flux surface, B.sub..theta.,o is the circumaxial magnetic field produced by said axial plasma current, ##EQU56## is the partial derivative of B.sub..theta.,o with respect to r, l is the number of said first windings, k is the wave number of the magnetic field produced by said first and second windings, I.sub.l (kr) is the modified Bessel function of order l, and I.sub.l (kr) is the derivative of I.sub.l (kr) with respect to its argument, q being defined as the average over a flux surface of the member of transits of the length of the plasma current by a magnetic flux line in making a single transit around the plasma current, and the absolute magnitude of q being less than 1 within said plasma current.