# CMAG: A Mission to Study and Monitor the Inner Corona Magnetic Field
## 1 Introduction
### Solar Corona Polarimetry  
Nowadays, the inference of magnetic fields from spectropolarimetric measurements of the forbidden coronal lines, Fe XIV 530 nm, Fe XI 789 nm, and Fe XIII 1074 nm, has become possible with the interpretation of the Zeeman, scattering, and Hanle effects [31; 32]. The Zeeman effect polarizes light from spectral lines due to the presence of magnetic fields in a moderate to strong regime. The Hanle effect, on the other hand, depolarizes light that is already polarized by scattering (or other physical mechanisms) in the presence of weak magnetic fields [33; 34]. To measure polarization in coronal lines, high-precision differential photometry is mandatory, and indeed, all four Stokes parameters of solar light must be measured. Quiet coronal line intensities (Stokes I; imaging) are one order of magnitude above the K-corona intensity at 1.10 R\({}_{\odot}\)[35]. Linear polarization signals (Stokes Q, U) are weaker, about 1 to 10% of the line core intensity, and hence subject to larger contamination by the already polarized solar corona (the so-called K-corona is linearly polarized by scattering to a large degree). Stokes V is even feebler than linear polarization (a few percent or per mille). Linear polarization is mainly proportional to the degree of anisotropy of the incident light coming from the solar disk, which depends on the height above the Sun's visible surface at where we observe, while the Stokes V amplitude is mainly proportional to the line-of-sight component of the field. Recent numerical models predict Stokes V amplitudes slightly above 0.1% in coronal loops for the Fe XIII 1074 nm line [32], in line with earlier predictions [36] that suggested amplitudes of about 0.5 \(\times\) 10\({}^{-3}\) for coronal loops and field strengths as low as 2 G. Therefore, measuring circular polarization in the corona is extremely challenging. Simple magnetographic calculations (see Figure 2) suggest signals barely above 0.1 % in the line emission of the quiet corona if the field is stronger than 10 G and when observing at 1.1 R\({}_{\odot}\). If one were to measure the magnetic field in locations further away from the solar limb, it would be necessary to focus on specific solar structures with higher density or significantly increase integration times. Hence, observations of magnetic fields in the inner corona are  
Figure 1: Simulated solar K-corona generated from a magnetohydrodynamic model. The field-of-view (red square) corresponds to 2.5 R\({}_{\odot}\), matching that of CMAG. very scarce. Those we currently have are severely limited in terms of spatial and temporal resolution. For example, [PERSON] and collaborators [37] obtained the first observations, requiring a spatial sampling of 20\({}^{\prime\prime}\) and a temporal integration of over an hour to detect circular polarization signals in the inner corona. Recent measurements suggest much stronger fields, in the range of 50-200 G, for cold and hot coronal loops [23; 38], hence predicting larger Stokes V signals in these structures. Coronal electron densities change from 10\({}^{9}\) cm\({}^{-3}\) at the bottom to 10\({}^{6}\) at 2 R\({}_{\odot}\). Therefore, the sensitivity of measurements decreases with distance. However, in loop structures, the density reaches 10\({}^{11}\) cm\({}^{-3}\), and emissivity is larger by one order of magnitude, making the signal-to-noise ratio (S/N) go up, hence increasing polarization sensitivity for equivalent exposure times. Electron density reaches 10\({}^{12}\) cm\({}^{-3}\) in flaring loops [1]. When more photons are available, CMAG will achieve the required polarization sensitivity in less time, with an FoV that covers from 1.02 to 2.5 R\({}_{\odot}\), and a spatial resolution of 2.5\({}^{\prime\prime}\) at 750 nm. Perhaps the most relevant aspect of the mission is that, in addition to its capabilities, it will take observations from space with unprecedented pointing stability, enabling the measurement of polarization signals in fainter solar structures.