{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/70885"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/70885","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Thermonuclear Driven Fast Magnetosonic Wave Heating in Tokamak Plasmas","abstract":"A thermonuclear driven fast magnetosonic wave instability is investigated in tokamak plasmas for propagation transverse to the external magnetic field at frequencies of several times the alpha particle gyro rate: (omega)(TURNEQ)L(OMEGA)(, ) =k(,(PERP))v(,A), L(TURN)4 to 8, k(,(PARLL))<<k(,(PERP)). The 2-D differential quasi-linear diffusion equation is derived in circular cylindrical, v(,(PERP))-v(,(PARLL)) geometry. We perform an expansion in the small parameter k(,(PARLL))/k(,(PERP)) of the quasi-linear diffusion coefficients. Examination of the mathematical structure of these coefficents reveals that they are independent of v(,(PARLL)) to zero order in the small parameter k(,(PARLL))/k(,(PERP)) and exhibit the ordering D(,(PERP)):D(,X):D(,(PARLL))(TURN)1:0(k(,(PARLL))/k(,(PERP))):0(k(,(PARLL))('2)/k(,(PERP))('2)) for the perpendicular, cross and parallel terms, respectively. Inherently 2-D phenomena such as loss cone and collisional effects are neglected and the isotropic Gaussian shell source is employed for the initial alpha distribution. These assumptions permit reduction of the problem from 2-D to 1-D by integrating out the v(,(PARLL)) dependence. This reduced system includes the contribution from all alpha particles. We have quantified the instability effect at the microscopic, plasma and system levels for the first time. System level information is available by coupling data produced in production runs of the 1-D formation with a 1 1/2-D tokamak transport code. We have employed a new technique to produce contour plots of the alpha particle threshold fraction to identify the instability regions in the n(,e)-T(,i) plane. Surveys of the n(,e)-T(,i) plane indicate that alpha particle threshold fractions as low as 10('-6)-10('-4) may be possible for the alpha source function in tokamak geometry. Plasma level survey calculations using the reduced 1-D quasi-linear formulation indicate enhancements in the classical alpha-ion energy split by factors of as much as 1.5 for T(,i)=T(,e) at 7 keV. System level effects, however, are less than a 1-2% improvement in fusion power, due to the rapid equilibration of electron and ion temperatures in these plasmas.","abstract_html":"A thermonuclear driven fast magnetosonic wave instability is investigated in tokamak plasmas for propagation transverse to the external magnetic field at frequencies of several times the alpha particle gyro rate: (omega)(TURNEQ)L(OMEGA)(, ) =k(,(PERP))v(,A), L(TURN)4 to 8, k(,(PARLL))<<k(,(PERP)). The 2-D differential quasi-linear diffusion equation is derived in circular cylindrical, v(,(PERP))-v(,(PARLL)) geometry. We perform an expansion in the small parameter k(,(PARLL))/k(,(PERP)) of the quasi-linear diffusion coefficients. Examination of the mathematical structure of these coefficents reveals that they are independent of v(,(PARLL)) to zero order in the small parameter k(,(PARLL))/k(,(PERP)) and exhibit the ordering D(,(PERP)):D(,X):D(,(PARLL))(TURN)1:0(k(,(PARLL))/k(,(PERP))):0(k(,(PARLL))('2)/k(,(PERP))('2)) for the perpendicular, cross and parallel terms, respectively. Inherently 2-D phenomena such as loss cone and collisional effects are neglected and the isotropic Gaussian shell source is employed for the initial alpha distribution. These assumptions permit reduction of the problem from 2-D to 1-D by integrating out the v(,(PARLL)) dependence. This reduced system includes the contribution from all alpha particles. We have quantified the instability effect at the microscopic, plasma and system levels for the first time. System level information is available by coupling data produced in production runs of the 1-D formation with a 1 1/2-D tokamak transport code. We have employed a new technique to produce contour plots of the alpha particle threshold fraction to identify the instability regions in the n(,e)-T(,i) plane. Surveys of the n(,e)-T(,i) plane indicate that alpha particle threshold fractions as low as 10('-6)-10('-4) may be possible for the alpha source function in tokamak geometry. Plasma level survey calculations using the reduced 1-D quasi-linear formulation indicate enhancements in the classical alpha-ion energy split by factors of as much as 1.5 for T(,i)=T(,e) at 7 keV. System level effects, however, are less than a 1-2% improvement in fusion power, due to the rapid equilibration of electron and ion temperatures in these plasmas.","abstract_has_math":false,"creators":["Sutton, William Roy, Iii"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T04:17:32Z","date_published":"2014-12-16T04:17:32Z","updated_at":"2026-07-22T22:26:03Z","subjects":["Engineering, Nuclear"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8302999"],"render_values":[{"text":"(UMI)AAI8302999","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/70885","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Sutton, William Roy, Iii"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T04:17:32Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Nuclear"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/70885","(UMI)AAI8302999"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A thermonuclear driven fast magnetosonic wave instability is investigated in tokamak plasmas for propagation transverse to the external magnetic field at frequencies of several times the alpha particle gyro rate: (omega)(TURNEQ)L(OMEGA)(, ) =k(,(PERP))v(,A), L(TURN)4 to 8, k(,(PARLL))<<k(,(PERP)). The 2-D differential quasi-linear diffusion equation is derived in circular cylindrical, v(,(PERP))-v(,(PARLL)) geometry. We perform an expansion in the small parameter k(,(PARLL))/k(,(PERP)) of the quasi-linear diffusion coefficients. Examination of the mathematical structure of these coefficents reveals that they are independent of v(,(PARLL)) to zero order in the small parameter k(,(PARLL))/k(,(PERP)) and exhibit the ordering D(,(PERP)):D(,X):D(,(PARLL))(TURN)1:0(k(,(PARLL))/k(,(PERP))):0(k(,(PARLL))('2)/k(,(PERP))('2)) for the perpendicular, cross and parallel terms, respectively. Inherently 2-D phenomena such as loss cone and collisional effects are neglected and the isotropic Gaussian shell source is employed for the initial alpha distribution. These assumptions permit reduction of the problem from 2-D to 1-D by integrating out the v(,(PARLL)) dependence. This reduced system includes the contribution from all alpha particles. We have quantified the instability effect at the microscopic, plasma and system levels for the first time. System level information is available by coupling data produced in production runs of the 1-D formation with a 1 1/2-D tokamak transport code. We have employed a new technique to produce contour plots of the alpha particle threshold fraction to identify the instability regions in the n(,e)-T(,i) plane. Surveys of the n(,e)-T(,i) plane indicate that alpha particle threshold fractions as low as 10('-6)-10('-4) may be possible for the alpha source function in tokamak geometry. Plasma level survey calculations using the reduced 1-D quasi-linear formulation indicate enhancements in the classical alpha-ion energy split by factors of as much as 1.5 for T(,i)=T(,e) at 7 keV. System level effects, however, are less than a 1-2% improvement in fusion power, due to the rapid equilibration of electron and ion temperatures in these plasmas.","Made available in DSpace on 2014-12-16T04:17:32Z (GMT). No. of bitstreams: 1 8302999.pdf: 6428123 bytes, checksum: 213b8fa74a435bcd5a53766ba0130bd4 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71051 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","236 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."]},{"key":"dc:title","label":"Title","values":["Thermonuclear Driven Fast Magnetosonic Wave Heating in Tokamak Plasmas"]}]}],"canonical_facts":{"dc:creator":["Sutton, William Roy, Iii"],"dc:date":["2014-12-16T04:17:32Z","10000-01-01","1982"],"dc:description":["A thermonuclear driven fast magnetosonic wave instability is investigated in tokamak plasmas for propagation transverse to the external magnetic field at frequencies of several times the alpha particle gyro rate: (omega)(TURNEQ)L(OMEGA)(, ) =k(,(PERP))v(,A), L(TURN)4 to 8, k(,(PARLL))<<k(,(PERP)). The 2-D differential quasi-linear diffusion equation is derived in circular cylindrical, v(,(PERP))-v(,(PARLL)) geometry. We perform an expansion in the small parameter k(,(PARLL))/k(,(PERP)) of the quasi-linear diffusion coefficients. Examination of the mathematical structure of these coefficents reveals that they are independent of v(,(PARLL)) to zero order in the small parameter k(,(PARLL))/k(,(PERP)) and exhibit the ordering D(,(PERP)):D(,X):D(,(PARLL))(TURN)1:0(k(,(PARLL))/k(,(PERP))):0(k(,(PARLL))('2)/k(,(PERP))('2)) for the perpendicular, cross and parallel terms, respectively. Inherently 2-D phenomena such as loss cone and collisional effects are neglected and the isotropic Gaussian shell source is employed for the initial alpha distribution. These assumptions permit reduction of the problem from 2-D to 1-D by integrating out the v(,(PARLL)) dependence. This reduced system includes the contribution from all alpha particles. We have quantified the instability effect at the microscopic, plasma and system levels for the first time. System level information is available by coupling data produced in production runs of the 1-D formation with a 1 1/2-D tokamak transport code. We have employed a new technique to produce contour plots of the alpha particle threshold fraction to identify the instability regions in the n(,e)-T(,i) plane. Surveys of the n(,e)-T(,i) plane indicate that alpha particle threshold fractions as low as 10('-6)-10('-4) may be possible for the alpha source function in tokamak geometry. Plasma level survey calculations using the reduced 1-D quasi-linear formulation indicate enhancements in the classical alpha-ion energy split by factors of as much as 1.5 for T(,i)=T(,e) at 7 keV. System level effects, however, are less than a 1-2% improvement in fusion power, due to the rapid equilibration of electron and ion temperatures in these plasmas.","Made available in DSpace on 2014-12-16T04:17:32Z (GMT). No. of bitstreams: 1 8302999.pdf: 6428123 bytes, checksum: 213b8fa74a435bcd5a53766ba0130bd4 (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71051 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","236 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."],"dc:identifier":["http://hdl.handle.net/2142/70885","(UMI)AAI8302999"],"dc:subject":["Engineering, Nuclear"],"dc:title":["Thermonuclear Driven Fast Magnetosonic Wave Heating in Tokamak Plasmas"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:03Z"}