An I2-promoted, metal-free domino protocol for one-pot synthesis of 1,3,4-oxadiazoles has been developed via oxidative cleavage of C(sp(2))-H or C(sp)-H bonds, followed by cyclization and deacylation. In this reaction, the use of K2CO3 as a base is found to be an essential factor in the cyclization and the C-C bond cleavage. This procedure proceeded smoothly in moderate to high yields with good functional group compatibility.
A new equilibrium pressure profile is proposed that extends the rigid rotor (RR) model with a simple unified expression P = P(ψ; β
s, α, σ) for both inside and outside the separatrix. A new method is described for solving the field-reversed configuration (FRC) one-dimensional (1D) equilibrium with only two parameters. The radial normalized FRC equilibrium profiles for pressure, magnetic field, and current density can be uniquely determined by the dimensionless parameters of
β
s
≡
P
s
/
B
e
2
/
2
μ
0
and δ
s ≡ L
ps/R
s. This modified rigid rotor (MRR) model has sufficient flexibility to accommodate narrow scrape-off layer (SOL) widths and hollow current density profiles, and can be used to fit experimental measurements. A database of 1D plasma equilibria in the (β
s, δ
s) space is provided for the convenience of real-time approximate FRC equilibrium reconstruction. The detailed one-dimensional (1D) characteristics of the equilibrium models are investigated analytically and numerically. The 1D results from the MRR models are also validated using two-dimensional (2D) Grad–Shafranov (G–S) equilibrium solutions.
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