## 1 Introduction  
Advances in medicine and technology have made it possible to produce brain images using magnetic resonance imaging (MRI). Moreover, improvements in MRI technology have led to image quality enhancements. A great deal of research has been invested in increasing the magnetic field strength of MRI systems with the objective of producing images with a higher signal-to-noise ratio (SNR) because increasing the magnetic field strength polarizes a larger number of protons, thereby producing stronger signals.  
Increasing the frequencies used in MRI systems, which results from the development of stronger magnets, requires the design of a radiofrequency (RF) coil that is capable of producing a field with high intensity and uniformity [1]. However, at higher frequencies, the \(1\,B_{1}^{+}\)! field uniformity is affected by wavelength shortening [2], and the performance of coils with high uniformity in smaller MRI systems, birdcage (BC) coils, for example, is reduced at higher frequencies [3].  
BC coils [4, 5, 6] are typically used in MRI experiments because they can generate a uniform magnetic field across their volume [7]. A BC coil consists of two rings with equal diameters that, although separated by a certain distance, are connected to each other by the coil legs. A BC coil with N legs has different resonant modes [8, 9]. In those modes, operating frequency can be predicted among other modes, such as ring modes [10], and is known to have more uniform \(1\,B_{1}^{+}\)! field distribution when the number of legs increases [11]. However, the BC coil underperforms when used in higher frequencies, because the magnetic field interacts with brain tissues that have different electromagnetic properties (conductivity and permittivity) [12]. The field uniformity is affected by shortened RF wavelengths and the resulting wavelength is significantly smaller than the imaging object, which is contrary to the case of using lower fields, leading significant field uniformity drop in 4.7T or higher [13]. Another field uniformity consideration is the electric (E) field,which can lead to local power absorption peaks in the tissues or in the measurement of the specific absorption rate (SAR), which is linked to localized tissue heating [14]. Generally, a uniform field yields a lower SAR values [15; 16; 17]. BC coils also follow these rules, with a higher frequency of the main magnet leading to reduced homogeneity and higher SAR for the produced field [18].  
This study proposes a BC design with a varying geometry to achieve better field intensity and uniformity compared with previously proposed asymmetric BC coils [19; 20; 21]. In the study by [22], the proposed BC coil utilizes an approximately elliptical shape to accommodate the upper body of a human subject, with the study concluding that a highly uniform field was achieved. Furthermore, in the study by [23], an asymmetric BC coil for small animals is proposed, for which half of the BC coil is offset by a certain distance. This modification to the conventional coil design provided an improved field distribution. The patent [24] describes a tampered birdcage coil for improved homogeneity, in which one of the BC rings is smaller than the other. In this study, a BC coil design that is nonsymmetrical with regard to the ring diameters is proposed to focus the magnetic field on the brain.