Global electromagnetic gyrokinetic simulations of internal transport barriers in reversed-shear tokamaks

Abstract Internal transport barriers (ITB) form through turbulence suppression, often observed when the safety factor profile exhibits an off-axis minimum. This work aims at improving our understanding of the conditions enabling the development of an ITB, using a more comprehensive physical model, including low- β electromagnetic flux-driven simulations. Our key findings are that electron dynamics is crucial for ITB formation even in an ITG scenario and that having q min close to a lowest order rational value (2 in our simulations) to allow for eddies self-interaction is a necessary ingredient. Electron dynamics has two critical effects. First, it leads to a structure formation characterized by strong zonal flows shearing rate, quench of turbulence (i.e. reduction of transport coefficients and fluctuation correlation) and profile corrugation. Second, it leads to zonal current sheets that result in a broadening of the minimum-q region, qualitatively consistent with the flux-tube simulations of Volčokas et al (2024 arXiv: 2412.01913 ). Flux-driven simulations performed with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>min</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> reveal the development of the transport barrier in the ion channel, forming at inner and outer radial positions with respect to the q min position. The ITB formation in flux-driven setup is not recovered if <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>min</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.03</mml:mn> </mml:mrow> </mml:math> . Additionally, a simulation at higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> indicates that the extent of the flattened region of the q -profile due to turbulent self-interaction does not change proportionally to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> or to ρ i , but somewhere in between. On the other hand, the input power required to achieve similar on-axis temperatures appears to exhibit almost gyro-Bohm scaling (for the two considered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mo>∗</mml:mo> </mml:msup> </mml:mrow> </mml:math> values). Furthermore, considering an initial q -profile with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>min</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.01</mml:mn> </mml:mrow> </mml:math> , flux-driven simulations show that partial self-interaction can evolve to complete self-interaction. This occurs due to turbulent-driven zonal currents that lower and flatten the q -profile down to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>q</mml:mi> <mml:mrow> <mml:mtext>min</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>2.0</mml:mn> </mml:mrow> </mml:math> , in line with what is reported in Volčokas et al (2024 arXiv: 2412.01913 ).