Tokamak is considered as the most promising experimental setup for achieving controllable nuclear fusion requirements. The parameter
$\beta_{\rm{N}}$
is an important parameter for tokamak devices: high
$\beta_{\rm{N}}$
benefits not only to plasma fusion but also to the enhancement of fusion reaction efficiency and the facilitation of steady-state operation. The HL-2A tokamak device has achieved stable plasma with
$\beta_{\rm{N}}$
exceeding than 2.5 through neutral beam injection heating, and transiently reached
$\beta_{\rm{N}}$
= 3.05, with a normalized density (
$n_{\rm{e,l}}/n_{\rm{e,G}}$
) of about 0.6, stored energy (
$W_{\rm{E}}$
) of around 46 kJ, and confinement improvement factor (
$H_{98}$
) of about 1.65. In this work, the integrated simulation platform OMFIT is used to analyze the plasma at
$\beta_{\rm{N}}$
= 2.83 and
$\beta_{\rm{N}}$
= 3.05, and the obtained
$W_ {\rm{E}}$
,
$n_{\rm{e,l}}/n_{\rm{e,G}}$
,
$H_{98}$
,
$\beta_{\rm{N}}$
, etc. are consistent with the experimental parameters. The bootstrap current (
$f_{\rm{BS}}$
) can reach to
$45{\text{%}}$
and
$46{\text{%}}$
. At both of the above moments, there are ion temperature double transport barrier (DTB) generated by the coexistence of internal transport barrier (ITB) and edge transport barrier (ETB), while high
$\beta_{\rm{N}}$
is usually related to DTB. In addition, the formation of ion temperature ITB in the HL-2A device is further analyzed, which is attributed to the dominance of turbulent transport in plasma transport, the suppression of turbulent transport in the core by fast ions and
${\boldsymbol E}\times{\boldsymbol B}$
shear, and the resulting improvement in confinement, thereby ultimately leading to the formation of ion temperature ITB. The ITB of ion temperature and the ETB of H-mode synergistically contribute to the creation of high
$\beta_{\rm{N}}$
plasma.
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