Hui Xie

Guillaume Andrieux
email: guillaume.andrieux@univ-nantes.fr

Yide Wang
email: yide.wang@univ-nantes.fr

Suili Feng
email: fengsl@scut.edu.cn

Zhiwen Yu

A Novel Threshold based Compressed Channel Sensing in OFDM System

Keywords: Channel estimation, compressed sensing, sparse channels with large delay spreads, orthogonal matching pursuit, OFDM, threshold

High speed data transmission for wireless communication in orthogonal frequency division multiplexing (OFDM) system requires eective channel state information (CSI). CSI should be precisely estimated with low consumption of spectral resources and acceptable computational cost. To realize this goal, an eective compressed sensing (CS) based channel estimation scheme is proposed for sparse channels with large delay spreads, without prior knowledge of channel statistics and noise standard deviation. By fully considering the rank of the measurement matrix, a novel algorithm based on orthogonal matching pursuit (OMP) and least squares (LS) methods with a new threshold is proposed for eective channel estimation. Simulation results show that with fewer number of pilots, the proposed method outperforms the compared existing channel estimation methods in a comprehensive way and approaches

Introduction

Orthogonal frequency division multiplexing (OFDM) technique is widely used in wireless communication system thanks to its advantages of high data transmission rate over multipath fading channel [START_REF] Bingham | Multicarrier modulation for data transmission: An idea whose time has come[END_REF]. In OFDM system, accurate channel state information (CSI), high spectral eciency, low complexity are all essential. Therefore, how to eectively balance the above factors is one of the main challenges in channel estimation eld.

In order to achieve the above goals, the sparse properties of physical channels can be exploited. The existence of physical sparse channels is proven by many experiments [START_REF] Bajwa | Compressed Channel Sensing: A new Approach to Estimating Sparse Multipath Channels[END_REF], which showed that digital television channels [START_REF] Minn | An investigation into time-domain approach for OFDM channel estimation[END_REF], underwater acoustic channels [START_REF] Berger | Application of compressive sensing to sparse channel estimation[END_REF], some particular urban channels for long term evolution system [START_REF] Maechler | Implementation of greedy algorithms for LTE sparse channel estimation[END_REF], Hilly Terrain channels [START_REF] Nasr | Performance of an echo canceller and channel estimator for on-channel repeaters in DVBT/H networks[END_REF] and ITU-R vehicular channels (channel A and channel B) [START_REF]International Telecommunication Union, Guidelines for evaluation of radio transmission technologies for IMT[END_REF] have sparse properties.

Traditional channel estimation methods are mainly based on least squares (LS) estimator. Due to the main drawback of LS, which tends to be highly aected by noise, especially in sparse channel situation, the most signicant taps (MST) based technique is developed [START_REF] Minn | An investigation into time-domain approach for OFDM channel estimation[END_REF]. For MST, dierent thresholds have been proposed for eective sparse channel estimation. There are generally two types of methods, the rst type requires the prior knowledge of channel statistics (power prole of channel impulse response (CIR) or sparsity level) [START_REF] Oliver | Sparse channel estimation in OFDM system by threshold-based pruning[END_REF][START_REF] Najjar | Sparsity level-aware threshold-based channel structure detection in OFDM systems[END_REF], while the second one relies on the estimated noise power or noise standard deviation (STD) [START_REF] Kang | Ecient DFT-based channel estimation for OFDM system on multipath channels[END_REF][START_REF] Xie | Ecient time domain threshold for sparse channel estimation in OFDM system[END_REF]. [START_REF] Rosati | OFDM channel estimation based on impulse response decimation: Analysis and novel algorithms[END_REF] shows that threshold without prior requirement of channel statistics will benet wireless communication system. A two-step threshold is proposed in [START_REF] Xie | Ecient time domain threshold for sparse channel estimation in OFDM system[END_REF], which realizes eective sparse channel estimation within a wide range of channel sparsity without prior knowledge of both channel statistics and noise STD.

The above mentioned methods assume that M ≥ L cp (M and L cp are the number of pilots and length of cyclic prex respectively), which leads to a signicant loss on frequency resources in estimating sparse channels with large delay spreads. Therefore, the case of M < L cp becomes more and more popular [START_REF] Tauböck | A compressed sensing technique for OFDM channel estimation in mobile environments: Exploiting channel sparsity for reducing pilots[END_REF]. The case of M < L cp is closely related to the compressed sensing (CS) [START_REF] Donoho | Compressed Sensing[END_REF] theory. l 1 norm based methods and greedy pursuit methods are two main categories of CS reconstruction methods [START_REF] Berger | Application of compressive sensing to sparse channel estimation[END_REF]. Compared with l 1 norm based methods, greedy pursuit methods have lower complexity, therefore, they are widely used in sparse channel estimation [START_REF] Berger | Application of compressive sensing to sparse channel estimation[END_REF][START_REF] Dai | Time domain synchronous OFDM based on simultaneous multi-channel reconstruction[END_REF][START_REF] Zhu | Sparsity-Aware Adaptive Channel Estimation Based on SNR Detection[END_REF][START_REF] Gao | Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO[END_REF]. Recently, orthogonal matching pursuit (OMP), one of the most popular algorithms among greedy pursuit methods and some of its derived algorithms, such as subspace pursuit (SP), adaptive simultaneous orthogonal matching pursuit (A-SOMP) and distributed sparsity adaptive matching pursuit (DSAMP) etc are used to realize channel estimation with prior knowledge of channel statistics (channel sparsity) or signal to noise ratio (SNR) or predetermined threshold [START_REF] Berger | Application of compressive sensing to sparse channel estimation[END_REF][START_REF] Dai | Time domain synchronous OFDM based on simultaneous multi-channel reconstruction[END_REF][START_REF] Zhu | Sparsity-Aware Adaptive Channel Estimation Based on SNR Detection[END_REF][START_REF] Gao | Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO[END_REF]. For example, in time domain synchronized OFDM (TDS-OFDM) system, SNR as a prior knowledge is used to estimate the channel sparsity S (number of non-zero channel taps) to improve the SP based sparse channel estimation [START_REF] Zhu | Sparsity-Aware Adaptive Channel Estimation Based on SNR Detection[END_REF]. In [START_REF] Gao | Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO[END_REF], by exploiting the spatially common sparsity within the system bandwidth of multicarrier massive MIMO chan-nels during multiple time blocks, the authors proposed distributed sparsity adaptive matching pursuit (DSAMP) algorithm to estimate the downlink channels. Of course, S max (maximum possible value of S) can be used [START_REF] Jiang | A fast algorithm for sparse channel estimation via orthogonal matching pursuit[END_REF], however, it may cause loss in estimation precision. We initially proposed an eective threshold estimator for CS based sparse channel estimation without optimizing the noise STD estimation [START_REF] Xie | A novel eective compressed sensing based sparse channel estimation in OFDM system[END_REF], selection of the m (m ≤ M ) columns in measurement matrix and error vector construction etc.

In this paper, we propose a novel threshold for OMP algorithm without prior knowledge of channel statistics and noise STD. The proposed threshold is based on a novel noise STD estimator, which is realized by a new error vector constructed by m selected coecients estimated by LS and initial CIR with S max coecients estimated by OMP which is dierent from our initial research work in [START_REF] Xie | A novel eective compressed sensing based sparse channel estimation in OFDM system[END_REF]. The proposed method allows estimating the real number of signicant taps S. Therefore, the error from the S max -S noise coecients can be eliminated. Simulation results show the eectiveness of the proposed method. This paper is organized as follows. The considered OFDM system model is given in section 2. In section 3, the proposed threshold based estimation algorithm for OMP is presented. Section 4 provides some simulation results. Conclusion is drawn in section 5.

System Model

Consider an OFDM system with N subcarriers, among which M are pilots with positions k 0 , k 1 , . . . , k M -1 . After the transmission of normalized

pilots X p = diag[x[k 0 ], x[k 1 ], . . . , x[k M -1 ]] through a S sparse channel h = [h[0], h[1], . . . , h[L cp -1]] T , the pilot vector y p = [y[k 0 ], y[k 1 ], . . . , y[k M -1 ]] T
is received at the receiver, and given by [START_REF] Bajwa | Compressed Channel Sensing: A new Approach to Estimating Sparse Multipath Channels[END_REF]:

y p = Ah + w p (1)
with A = X p F M ×Lcp the measurement matrix; In the case of M < L cp , we have Rank(A) < L cp . To obtain an eective threshold, the noise STD is required. However, due to Rank(A) = M , reconstruct the whole CIR with length L cp and estimate the noise STD are impossible. In this case, partial CIR with m (m ≤ M ) coecients can be extracted to estimate the noise STD.

F M ×Lcp (k u , v) = e -j(2πkuv/N ) , 0 ≤ u ≤ M -1, 0 ≤ v ≤ L cp -1; w p = [w[k 0 ], w[k 1 ], . . . , w[k M -1 ]]
(1) can be rewritten as:

y p = A m h m + A b h b + w p (2)
where

A m = [a[p 0 ], a[p 1 ], . . . , a[p m-1 ]] and h m = [h[p 0 ], h[p 1 ], . . . , h[p m-1 ]] T
are the matrix with the m selected columns of A, which is used to realize the Fourier transform of the partial CIR and vector with the m corresponding channel taps of h, which contains the partial information of CIR respectively;

A b and h b = [h[p m ], h[p m+1 ], . . . , h[p Lcp-1 ]
] T are the matrix with the remaining L cp -m columns of A and vector with the corresponding channel taps of h respectively.

Using LS to estimate the m selected channel taps, we get:

ĥls_m = (A H m A m ) -1 A H m y p (3)
Combining ( 2) and (3), we have:

ĥls_m = h m + (A H m A m ) -1 A H m A b h b + (A H m A m ) -1 A H m w p (4)
which is composed of three parts, the rst part is the m selected channel taps, the second one is the interference due to the signicant taps in h b and the last part is the noise part denoted by e m .

In order to obtain a good estimate of the error vector e m for eective noise STD estimation, two aspects are essential. The rst one is the selection of the number of m and the m columns, which will be discussed in Section 4 and Section 3.1.1 respectively, the second one is the reduction of the interference from the rst two parts in (4), which will be discussed in Section 3.1.2.

Selection of m Columns

The condition number of A m is a key parameter for LS method. The smaller it is, the better is the stability of the estimator to perturbations [START_REF] Mostovyi | On the stability the least squares Monte Carlo[END_REF].

To obtain the m eective selected columns, cond(A m ) should be the smallest possible. To realize this, the subset with m indices should be chosen as:

Λ = arg min Λ 1 cond(A Λ 1 ), |Λ 1 | = m (5)
with Λ the subset of the m optimally selected columns. The optimal partial measurement matrix denoted by A m is obtained by choosing the m columns dened by Λ.

(5) is the optimal solution for the estimation of h m , however, to obtain Λ, there are Lcp m possible choices. It is a heavy computational task. Similar to the suboptimal pilot arrangement method proposed in [START_REF] He | Pilot pattern optimization for compressed sensing based sparse channel estimation in OFDM systems[END_REF], a suboptimal subset of indices of m selected columns can be obtained. Firstly, a limited number of subsets of m selected columns are randomly generated, then, the suboptimal subset is given by the matrix with the smallest condition number.

Reduction of Interference and Construction of Error Vector

In order to get a good estimate êm , it is necessary to reduce the impact of the signicant taps of h m and h b in (4). Therefore, the signicant taps estimated by OMP expressed by ĥomp

[d 0 ], ĥomp [d 1 ], . . . , ĥomp [d Smax-1 ], 0 ≤ d 0 , d 1 , ..., d Smax-1 ≤ L cp -
êm =h m -ĥomp_m + (A H m A m ) -1 A H m A b (h b -ĥomp_b ) + (A H m A m ) -1 A H m w p = ĥls_m -ĥomp_m -(A H m A m ) -1 A H m A b ĥomp_b (6)
From ( 4) and ( 6), êm can nally be rewritten as:

êm = ĥls_m -I m (A H m A m ) -1 A H m A b   ĥomp_m ĥomp_b   (7)

Noise STD and Threshold Estimation

If the initial estimated channel by OMP is accurate, êm approximates the noise vector e m = (A H m A m ) -1 A H m w p with length of m. Each element of e m being a linear combination of independent complex Gaussian variables, is a complex Gaussian random variable. In practice, some small contribution of signicant taps remains in êm , it is better to use the median absolute deviation (MAD) method [START_REF] Xie | Ecient time domain threshold for sparse channel estimation in OFDM system[END_REF][START_REF] Donoho | Ideal spatial adaptation by wavelet shrinkage[END_REF]. In the following, MAD method is adopted to realize eective noise STD estimation.

Each element of e m follows complex Gaussian distribution. The STD of its real part σr and imaginary part σi is estimated by the median value [11]:

σr = σi = σ = median(|ê m |) √ ln4 (8)
Therefore, the STD of each element of e m can be estimated by σ = √ 2σ . With the estimated σ, the universal threshold can be adopted for the detection of sparse channel [START_REF] Bajwa | Compressed Channel Sensing: A new Approach to Estimating Sparse Multipath Channels[END_REF][START_REF] Xie | Ecient time domain threshold for sparse channel estimation in OFDM system[END_REF][START_REF] Donoho | Ideal spatial adaptation by wavelet shrinkage[END_REF]:

T = Rσ; (R = 2(1 + a)ln(L cp )) (9)
with a, (a ≥ 0) a constant factor. In this paper, we take a = 0.

S

Find the estimated error vector by ( 7) Step 1: Get an initial CIR with S max iterations by OMP algorithm.

p y LS estimation (selected channel taps) _ ˆ[0] ls m h _ ˆ[ 1] ls m h m  ˆT R   ˆ[0] h ˆ[ 1] cp hL  _ ˆ[0] omp b h _ ˆ[ 1] omp b cp h L m            ˆ[0] m e ˆ[ 1] m e m     _ ˆ[0] omp m h _ ˆ[ 1] omp m h m  ˆm e    m
Step 2: Estimate the partial CIR with y p by LS (3).

Step 3: Obtain the estimated error vector êm by (7).

Step 4: Estimate the noise STD σ from ( 8) and the threshold T by [START_REF] Najjar | Sparsity level-aware threshold-based channel structure detection in OFDM systems[END_REF].

Step 5: Detect the MST by: ĥ

[n] =    ĥomp [n], | ĥomp [n]| > T 0, | ĥomp [n]| ≤ T , 0 ≤ n ≤ L cp -1 (10)

Simulation Results

In simulation, a QPSK modulated OFDM system with length of cyclic prex 256, is considered. The system has a total bandwidth of 10MHz [START_REF] Najjar | Sparsity level-aware threshold-based channel structure detection in OFDM systems[END_REF] and 1024 subcarriers, among which minimum 128 are pilots. For obtaining a comprehensive performance evaluation of dierent channel estimation methods, two dierent sparse channel models with dierent channel sparsities and channel statistics are considered. The rst channel model is the ATTC (Advanced Television Technology Center) and the Grand Alliance DTV laboratory's ensemble E model whose CIR is given by [START_REF] Minn | An investigation into time-domain approach for OFDM channel estimation[END_REF]:

h[n] = δ[n]+0.3162δ[n-2]+0.1995δ[n-17]+0.1296δ[n-36]+0.1δ[n-75]+0.1δ[n-137]. (11)
where the unit delay of the channel is equal to the OFDM sample period.

The second channel model is the Hilly Terrain channel [START_REF] Nasr | Performance of an echo canceller and channel estimator for on-channel repeaters in DVBT/H networks[END_REF] whose power delay prole (POD) is given in Table 1.

The coecients in [START_REF] Xie | Ecient time domain threshold for sparse channel estimation in OFDM system[END_REF] and the square root of the elements of the relative power in their linearized form in Table 1 represent the STD of the corresponding zero mean complex Gaussian random variables. Additionally, the timation methods for the rst channel model. We observe that even with only 12.5% of pilots, the proposed method signicantly outperforms the LS method with the threshold proposed by Kang et al. [START_REF] Kang | Ecient DFT-based channel estimation for OFDM system on multipath channels[END_REF] (for convenient comparisons, the exact noise STD is used) with 25% of pilots and OMP method with 20 taps and 12.5% of pilots throughout the considered E b /N 0 ;

the E b /N 0 gap is about 2dB for the same BER performance. Additionally, the proposed method slightly outperforms the LS estimator with sub-optimal threshold (SOT) [START_REF] Rosati | OFDM channel estimation based on impulse response decimation: Analysis and novel algorithms[END_REF] (the estimated number of channel taps Ŝ is set to be the channel sparsity S) and 25% of pilots in the overall considered E b /N 0 , however, the spectral eciency of the proposed method is much better. Furthermore, without prior knowledge of either channel statistics and noise STD, the proposed method still maintains good performance on BER compared with sparsity adaptive matching pursuit (SAMP) method (step size s = 1) [START_REF] Do | Sparsity adaptive matching pursuit algorithm for practical compressed sensing[END_REF] with the prior knowledge of noise STD and 12.5% of pilots, OMP method with 6 taps (exact sparsity S in the rst channel model), the oracle estimator (constrained LS with known number of non-zero channel coecients and their positions) [START_REF] Ben-Haim | Coherence-based performance guarantees for estimating a sparse vector under random noise[END_REF] and known channel CSI (known instantaneous channel frequency response). When compared with SAMP method, the oracle estimator with 12.5% of pilots and known CSI, the proposed method has at most 0.15dB, 0.5dB and 0.8dB performance degradation respectively.

+ 10log(n b N -M N N N +Lcp ) = E b /N 0 + 1.
46dB in the case of 12.5% of pilots (For QPSK modulation, one symbol contains 2 bits, so n b = 2. Additionally, in the case of 12.5% of pilots, M = 128), while in the case of 25% of pilots, SNR = E b /N 0 + 0.79dB (The same calculation formula, but in the case of 25% of pilots, M = 256), the power payload of the methods with 25% of pilots is 0.67dB higher than that of the methods with 12.5% of pilots. If we consider the LS estimator with SOT and 25% of pilots in 6dB and the oracle estimator with 12.5% of pilots in 5.33dB in the small gure in

BER

Proposed method (m=20,12.5% pilots) Proposed method (m=40,12.5% pilots) Proposed method (m=60,12.5% pilots) Proposed method (m=80,12.5% pilots) Proposed method (m=100,12.5% pilots) Proposed method (m=120,12.5% pilots) (σ is the exact noise STD, σi is the proposed estimated STD in the i th Monte-Carlo simulation and U is the number of Monte Carlo simulations), which is shown in Table 2. when m = 100, the condition number is 9.29, which is a bigger number, however, it is not a too big value for condition number, therefore, ε dierence is also limited. However, when m = 120 close to the number of pilots 128, the condition number of A m is 24.71, which is nearly 5 times as large as that for m = 80. This can explain why the noise STD estimation and BER performance are poor when m = 120.

From the above analysis combined with the performance of the proposed noise STD estimation method with dierent m in Table 2 and the condition number of A m in Table 3, we know that the choice of the value of m should eectively balance the number of noise samples m and the condition number of A m . In practice, m/M should be considered. In this paper M = 128.

The cases m = 60 and m = 80 can achieve the best noise STD performance.

Therefore, a good value for m/M should be within the range [0.47, 0.63].

Table 4 evaluates the complexity of the proposed method and the traditional DFT based method. As can be seen from the table, the complexity of the proposed method is composed of that of OMP method O(M L cp S max ), threshold estimation method O(M 2 m) and FFT method O(N log 2 N ). In the is O(N log 2 N ), therefore, the total complexity is O(N log 2 N ). Although, the proposed method has a higher complexity than LS based method, the estimation performance and spectral eciency of the proposed method are much better than LS based method. (Note: The complexity of the algorithm of condition number based m columns selection and that of pilot arrangement is not included, because they can be realized in the absence of practical communication.) SAMP method (s = 1) requires a few more iterations than OMP as indicated in [START_REF] Do | Sparsity adaptive matching pursuit algorithm for practical compressed sensing[END_REF], so the complexity of SAMP is higher than the proposed method, which is also conrmed by the simulation time. Additionally, SAMP method requires the prior knowledge of noise STD, although its estimation performance is slightly better.

Conclusion

This paper addresses the CS based sparse channel estimation in OFDM system. The main goal of the paper is to detect MST for CS based sparse channel estimation without prior knowledge of channel statistics and noise STD. In the proposed method, by employing jointly LS and OMP, an error vector with m coecients, which approximates the noise vector, is constructed. By employing the m coecients of the error vector, the noise STD is estimated and eective MST detection is realized. Simulation results

show that the proposed method has the advantages in comprehensive performances regarding the channel estimation performance, spectral eciency, computational complexity and prior parameters dependence (noise STD).

1

 1 are introduced. The signicant taps of ĥomp in subsets Λ and Λ c (the complement of Λ) are extracted to get two new sparse vectors ĥomp_m and ĥomp_b . Then, a new equation is obtained with regard to êm :

Figure 1 :

 1 Figure 1: Proposed channel estimation method

3 Figure 2 :

 32 Figure 2: BER performance comparison for the rst channel model

Figure 3 :Figure 4 :

 34 Figure 3: BER performance comparison for the second channel model

Fig 2 ,

 2 their BER performance is the same and E b /N 0 gap is about 0.67dB, which actually corresponds approximately to the power payload gap. Additionally, considering the same channel estimation performance, the E b /N 0 gap between the LS estimator with SOT and 25% of pilots and the oracle estimator with 12.5% of pilots in Fig 2 is less than 0.6dB within the E b /N 0 range 10dB-20dB, which can explain why the LS estimator with SOT and 25% of pilots has better performance in MSE. The above analysis on the performance of the proposed method considers m = 80. To show the inuence of the value of m, in Fig 5, the BER performance of the proposed method with dierent m for the rst channel model is shown. Generally, the proposed method with m = 20, 40, 60, 80, 100 and 12.5% of pilots has almost the same BER performance throughout the

Figure 5 : 1 i=0

 51 Figure 5: BER performance of proposed methods with dierent m for the rst channel model

Table 1 :

 1 Power delay prole for 12 tap Hilly Terrain channel

	Delay [µs]	0 0.2 0.4 0.6 0.8 2.0 2.4 15 15.2 15.8 17.2 20
	Power [dB] -10 -8 -6 -4	0	0	-4 -8	-9	-10 -12 -14
	pilot pattern arrangement is obtained by the suboptimal method proposed in
	[21]. Moreover, we consider S max = 20 and 6000 randomly generated subsets
	of indices are used for searching a suboptimal subset of indices selection of
	m selected columns.
	10 -2
	10 -3	4	6	8	10	12		14	16	18	20
						E

b /N 0 (dB) BER Proposed method (12.5% pilots) OMP (20 taps and 12.5% pilots) OMP (6 taps and 12.5% pilots) Oracle estimator (12.5% pilots) LS (threshold of Kang et al [10] 25% pilots) LS (suboptimal threshold (SOT) [12] 25% pilots) SAMP [23] (s=1 and 12.5% pilots) Known channel knowledge

Table 2 :

 2 Performance of the proposed noise STD estimation method with dierent m for As can be seen from Table2, for the same value of m, ε is extremely stable for dierent E b /N 0 . When m = 60, 80, ε is approximately 0.11. However, when m = 120, ε is 1.64, which is a huge error for noise STD estimation.

	the rst channel model
	E b /N 0 (dB) m = 20 m = 40 m = 60 m = 80 m = 100 m = 120
	10	0.24	0.19	0.11	0.11	0.37	1.64
	20	0.24	0.18	0.11	0.11	0.38	1.64
	30	0.23	0.18	0.11	0.11	0.38	1.64

Table 3 :

 3 Condition number of the measurement matrix A m

	m	20	40	60	80	100	120
	condition number 1.66 2.43 3.55 5.26 9.29 24.71

Table 3

 3 presents the condition number of A m with dierent m. When m = 20, 40, 60, 80, the condition number of A m is less than 5.5. Comparatively,

Table 4 :

 4 Computational complexity comparisoncp S max ) O(N log 2 N ) O(M log 2 M ) O(N log 2 N )proposed method, the complexity of OMP algorithm is O(M L cp S max ), which approximates to O(M 2 m), therefore, the total complexity of the proposed method is O(M L cp S max ) + O(N log 2 N ). LS based method has complexity of LS estimator, threshold estimation and FFT method. The complexity of LS and threshold methods is O(M log 2 M ) and the complexity of FFT method

		Proposed Method	LS based method
	Alg	OMP+Thr	FFT	LS+Thr	FFT
	Comp O(M L

Acknowledgment This work was supported by China Scholarship Council (No. 2010615039), Research Fund of Tianjin University of Technology and Education (No. KRKC 011614 and No. KJ15-16) and Science and Technology Planning Project of Guangdong Province, China (No. 2015A050502011 and No. 2016A010101009).


S Tigrine
email: sarah.tigrine@latmos.ipsl.fr

N Carrasco

L Vettier

G Cernogora

A microwave plasma source for VUV atmospheric photochemistry

Keywords:

Microwave plasma discharges working at low pressure are nowadays a welldeveloped technique mainly used to provide radiations at different wavelengths. The aim of this work is to show that those discharges are an efficient windowless VUV photon source for planetary atmospheric photochemistry experiments. To do this, we use a surfatron-type discharge with a neon gas flow in the mbar pressure range coupled to a photochemical reactor. Working in the VUV range allows to focus on nitrogen-dominated atmospheres (λ < 100 nm). The experimental setup makes sure that no other energy sources (electrons, metastable atoms) than the VUV photons interact with the reactive medium. Neon owns two resonance lines at 73.6 and 74.3 nm which behave differently regarding the pressure or power conditions. In parallel, the VUV photon flux emitted at 73.6 nm has been experimentally estimated in different conditions of pressure and power and varies in a large range between 2×10 13 ph/s/cm 2 and 4×10 14 ph/s/cm 2 which is comparable to a VUV synchrotron photon flux. Our first case study is the atmosphere of Titan and its N2-CH4 atmosphere. With this VUV source, the production of HCN and C2N2, two major Titan compounds, is detected, ensuring the suitability of the source for atmospheric photochemistry experiments.

Introduction

Microwave plasma columns are widely used this is why developing an effective source has become an important topic over the past decades. In the 1970s, Moisan et al [START_REF] Moisan | A new HF device for the production of long plasma columns at a high electron density[END_REF] [START_REF] Moisan | A Small Microwave Plasma Source for Long Column Production without Magnetic Field[END_REF]) created the first surface-wave launcher, called "surfatron", working in the microwave range, which is an efficient and compact tool for creating long plasma columns in a wide range of pressures (from atmospheric pressure to fractions of mbar) and discharge diameters. One of the main advantages of those discharges is that they are electrodeless and then avoid pollution by metal sputtering. They are also reliable reservoirs of charged, reactive particles and radiation [START_REF] Moisan | Plasma sources based on the propagation of electromagnetic surface waves[END_REF]. The individual wavelength of these radiations depends on the gas used for the discharge. It goes from the infra-red up to the vacuum ultra-violet (VUV) range (below 200 nm) as shown by [START_REF] Espinho | Vacuum ultraviolet emission from microwave Ar-H2 plasmas[END_REF]) [START_REF] Espinho | Extreme ultraviolet radiation emitted by helium microwave driven plasmas[END_REF] in their studies of the VUV emission of an Ar-H2 gas mixture or an helium discharge.

The radiations are mostly used as light sources for different technical studies. For example, a low pressure Kr VUV source is used for its photoionization efficiency, as an alternative to electronic impact in mass spectrometers, in order to avoid complex fragmentation patterns [START_REF] Northway | Demonstration of a VUV Lamp Photoionization Source for Improved Organic Speciation in an Aerosol Mass Spectrometer[END_REF]). At atmospheric pressure, surface-wave driven plasma find applications in surface treatment, as they increase the wettability of silicon [START_REF] Hnilica | Surface treatment by atmospheric-pressure surfatron jet[END_REF].

The aim of the present work is to develop a low-pressure (mbar) microwave plasma discharge (2.45 GHz) in a noble gas used as a VUV light source for a new application: to perform laboratory simulations of the planetary atmospheric photochemistry occurring at high altitudes, where solar VUV photons are penetrating. This wavelength range is of high demand in photochemistry laboratory simulations as it permits the dissociation and/or ionization of a lot of molecules, involving molecular nitrogen, the most abundant component in the atmospheres of the Earth and of Titan, the largest satellite of Saturn, on which we will focus here. As a matter of fact, thanks to the Cassini-Huygens mission (NASA-ESA), it is known now that Titan's atmosphere is mainly composed of N2 and CH4 for a methane concentration between 2 and 10 %, depending on the altitude [START_REF] Waite | The process of tholin formation in Titan's upper atmosphere[END_REF]). The observations revealed that a complex organic chemistry takes place in this 1200 km wide atmosphere, all starting with the dissociation and ionization of the neutrals N2 and CH4 by the VUV solar radiations in the upper layers.

The fast and efficient photochemistry leads to the formation of heavy C and/or N based species, like benzene (C6H6) or pyridine (C5H5N) for example. They will then grow into aerosols that globally surround the whole satellite on several hundreds of kilometres. All those processes make Titan a natural laboratory to witness and understand this complex organic chemistry but despite all the data collected, all the possible photochemical pathways in such a hydrocarbon nitrogen rich environment are not precisely understood. This is why Titan's atmospheric photochemistry experiments are of high interest. So far, the main VUV sources have been Mercury lamps at 253.65 nm [START_REF] Clarke | The Design and Use of a Photochemical Flow Reactor: A LaboratoryStudy of the Atmospheric Chemistry of Cyanoacetylene on Titan[END_REF] or Hydrogen lamps emitting the Ly-α line at 121.6 nm which is the main source of VUV energy in the solar system [START_REF] Thuillier | Solar irradiance reference spectra for two solar active levels[END_REF]. Those lamps allow to work in closed gas cells as MgF2 windows are transparent to radiations above 110 nm and focus on the kinetics of heavy hydrocarbon formation (Ádámkovics 2003), or on the influence of benzene (C6H6) on Titan's atmospheric chemistry [START_REF] Yoon | The role of benzene photolysis in Titan haze formation[END_REF]. Also, a gas mixture of H2-He was used in various conditions in order to obtain an output comparable to the solar irradiance between 115 and 170 nm [START_REF] Es-Sebbar | Optimization of a Solar Simulator for Planetary-Photochemical Studies[END_REF].

Nevertheless, molecular nitrogen requires wavelengths shorter than 100 nm in order to allow a direct photo-dissociation (Figure 1). This implies that the flows on both sides have to be balanced as the gas reactor and the VUV source would be openly coupled. So far, one way to obtain a VUV intense photon source has been coupling a gas reactor to a VUV synchrotron beamline [START_REF] Imanaka | Formation of nitrogenated organic aerosols in the Titan upper atmosphere: SI[END_REF], [START_REF] Peng | Titan's atmosphere simulation experiment using continuum UV-VUV synchrotron radiation[END_REF]. But even if they allow a high photon flux and a large range of specific energies [START_REF] Nahon | DESIRS: A state-of-the-art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL[END_REF], they provide only a limited duration for the experimental campaigns as the demand has exponentially increased in the past decades.

Still in the VUV range, an alternative could be commercial lamps, which exist in different types and shapes. Most of them are based on plasma discharge techniques involving noble gases. A priori, they offer several experimental qualities like a high intensity VUV beam (10 15 ph/s) or a low-pressure discharge (lower than few mbar). Nevertheless, these set-ups do not provide the flexibility needed in terms of wavelength and pressure that atmospheric photochemistry experiments demand. In fact, the Solar system offers a wide range of atmospheres which do not share the same conditions, especially regarding the pressures. The VUV source, which is to be window-less coupled to the photochemical reactor, has to suit an Earth-like stratospheric pressure as well as Titan's ionosphere conditions. For example, the Scienta VUV 5000 focuses only on the extreme UV helium lines at 58.4 nm, 53.7 nm (He I) and 30.4 nm (He II). Or the UVS40 A2 source from Henniker Scientific is designed to be only coupled with experiments at pressures lower than a few 10 -2 mbar, which makes it inappropriate for some experimental simulations of atmospheric photochemistry.

For this kind of applications, new window-less VUV sources are required and flexible low-pressure microwave discharges could be a solution, explored in the present work. We test here the potential of the surfatron technique with our experimental setup. One of the main aims is to ensure that no other energy source than VUV radiations could reach the reactor and initiate some unwanted chemistry. The other energy sources to avoid are electrons from the plasma discharge and metastable atoms.

A complete diagnosis of the system is then performed regarding the flux of photons delivered by the VUV lamp in different conditions of pressure and power, in order to compare it with the flux of other VUV sources like synchrotron facilities. Conclusions regarding its suitability for pure atmospheric photochemistry experiments are then drawn, with the application to the upper atmosphere of Titan.

Experimental setup

The VUV source: a microwave-plasma discharge

The plasma discharge takes place in a 40 cm length tube in fused silica with an internal diameter of 8 mm and an external diameter of 10 mm, surrounded by a surfatron resonance cavity. The microwave power delivered by a Sairem generator goes up to 200 W. The surfatron can be moved along the quartz tube in order to settle the end of the discharge regarding the entrance of the photochemical reactor. A compressed air circulation avoids any over heat of the system. Surface temperature measurement showed that it does not go above 60°C. The gas flow is regulated with a 0-10 sccm (cm 3 /min STP) range MKS mass flow controller. Moreover, the pressure is measured with a Pfeiffer capacitor gauge, mounted upstream the surfatron device, while the main part of the plasma column is created downstream the field applicator.

Three noble gases, with intense resonance lines, can be used in order to work in the VUV range. Argon emits at 104.8 nm (no dissociation of N2), neon at 73.59 and 74.37 nm and helium at 58.4 and 53.7 nm (ionization of both molecules) (table 1). Here, we use neon: at this energy, the dissociation and ionization of N2 are both possible (figure 1) in parallel to the ionization of CH4 (threshold at 98.52 nm).

Characterization of the source with a VUV monochromator

The characterization of the VUV source is performed by coupling it directly to a VUV 1 m focal length McPherson NOVA 225 spectrometer, fitted with a 1200 gr/mm concave grating blazed at 45 nm and sensitive from 30 nm to 300 nm. The efficiency of the grating strongly varies with the wavelength and is around 6 % at 75 nm (characterized by McPherson). In order to avoid the saturation of the acquisition system but still have a good resolution, the width of the slits is set up at 75 µm for a height of 4 mm. The acquisition system consists of an Optodiode AXUV100 photodiode coupled to an amplifier. The output signal gives 1 V for 1 nA and saturates at 10 V. Moreover, according to the data sheet, at 75 nm, the photodiode responsivity is about 0.22 A/W.

The monochromator is pumped with a turbomolecular pump (Agilent TV 301) and the internal pressure is measured by a Penning gauge (Oerlikon) calibrated for air. The real pressure is obtained using a neon/air correction factor. The turbomolecular pump ensures an ultimate vacuum of 10 -8 mbar inside the monochromator; while the VUV source is also pumped by this system, through the entrance slit. At the maximum gas flow injected into the VUV source, the monochromator pressure is about 10 -3 mbar.

The luminous power collected by the photodiode is related to the number of photons per second:

𝑑𝐸 𝑑𝑡 = ℎ𝑐 𝜆 × 𝑑𝑁 𝑝 𝑑𝑡 (1)
where E is the energy and Np the number of collected photons.

As neon from the source is pumped in the monochromator, optical absorption happens. Then the transmission inside the monochromator at a specific pressure is given by the Beer-Lambert law:

𝐼 𝑡 𝐼 0 = 𝑒 -𝑑×[𝑁𝑒]×𝜎 (2)
where d stands for the length of the optical path (here d = 2 m); σ is the absorption cross section (for neon and around 75 nm, σ = 9 × 10 -17 cm² [START_REF] Hébrard | Coupled noble gas-hydrocarbon evolution of the early Earth atmosphere upon solar UV irradiation[END_REF])); and finally [Ne] is the neon density linked to the pressure via the perfect gas law. In the few cm between the end of the discharge and the monochromator entrance slit, the absorption is negligible.

After weighting the number of photons per second with all those factors (responses of both the photodiode and the grating, plus the neon absorption), we divide by the surface of the exposed slits in order to obtain the photon flux (ph/s/cm²).

The atmospheric photoreactor ("APSIS")

The table-top VUV source is to be coupled with a photochemical reactor named APSIS (Atmospheric Photochemistry SImulated by Surfatron) in order to carry research on planetary upper atmospheres and their interaction with the VUV solar light. The APSIS reactor is described in details in [START_REF] Carrasco | VUV photochemistry simulation of planetary upper atmosphere using synchrotron radiation[END_REF]. Briefly, it is a stainless steel chamber of dimensions 500 mm x 114 mm x 92 mm where the reactive mixture is introduced via a gas inlet (figure 2). The gas mixture is chosen in order to simulate Titan's atmospheric composition. In the present work, a 95-5% N2-CH4 mixture is injected up to 10 sccm with a MKS gas flow controller. Before each experiment, the reactor is pumped by a turbomolecular pump down to 10 -7 mbar. During the photochemistry experiments, a rotary vane pump ensures a stable pressure on the order of 1 mbar.

In-situ mass spectrometry on APSIS

We use mass spectrometry to monitor the neutral molecules in the experiment, with a HIDEN HPR-20 QIC mass spectrometer. The gaseous products are taken at the closest spot from the VUV source. In order to maintain a low pressure inside the mass spectrometer at 10 -7 mbar, a 1 m capillary tube with an internal diameter of 1/16e inch is used. The Multiple Ion Detection (MID) mode on the mass spectrometer is chosen, as it follows selected mass signals in function of time and shows the evolution of the intensities before and during the irradiation process.

UV optical emission spectroscopy on the coupled system "VUV source-APSIS"

In order to ensure that no neon plasma enters the APSIS reactor, and that the dissociation of nitrogen and methane only occurs from the VUV photochemistry, optical emission spectroscopy of the neon-N2-CH4 system is performed in the UV range. A Hamamatsu spectrometer TG-UV C9404CAH is positioned in front of the VUV source at the opposite side of the reactor (figure 2). The emitted spectra in the UV range from 200 nm to 450 nm is recorded through a quartz window.

Results

Validation of pure photochemistry

In order to work with a clean neon plasma, the discharge remains on for at least 20 min before starting any measurement. A VUV spectrum of the clean discharge is presented on figure 3 (black curve). The key parameter in our photochemistry experimental platform is the distance between the end of the discharge and the entrance of the reactor. Indeed, if the distance is too short, there is a risk that the discharge would continue inside the reactor and create a N2-CH4 plasma (electron-driven chemistry) or that the metastable neon atoms will enter the reactor. But if the distance is too long, a photon loss is to be considered.

1.1.1 Preventing electron-driven chemistry. Thanks to optical emission spectroscopy, it is possible to monitor the N2 bands of the Second Positive System (SPS), which are recognizable because degraded to shorter wavelengths. The SPS is emitted from the 𝑁 2 (𝐶 3 𝛱 𝑢 ) state which cannot be populated neither by the 73.6 nm nor the 74.3 nm VUV line. This emission is then due to the energetic electrons of the plasma in the reactor: seeing those SPS bands means that the plasma discharge enters the photo-reactor and interacts with the N2-CH4 mixture.

First, in order to inject the maximum amount of VUV photons, the surfatron has been placed as near as possible from the entrance of the APSIS reactor. However, in this configuration, N2 bands of the SPS appear on the spectrum (Figure 3, red curve).

It is then relevant to balance the distance from the end of the discharge and the entrance of the reactor in order to have enough photons entering the reactive medium without exciting the nitrogen-methane mixture. For this reason, the surfatron is pushed back from the entrance of the reactor until the end of the discharge is 5 cm away from it. Figure 4 compares UV spectra of the only neon source and the APSIS reactor filled with N2-CH4 and irradiated by the surfatron source in its new position. N2 emission bands are no more observed, even for the maximum (10 sccm) gas flow of N2-CH4. From that we can conclude that N2 is not excited by electrons, and that there is no electron-driven chemistry in the reactor with this position of the surfatron.

1.1.2 Preventing neon metastable atom driven chemistry. Another possible source of energy could also be the neon metastable states 3 P 0 2-0 at 16.61 and 16.71 eV. Those metastable atoms are a potential source of energy for ionizing molecular nitrogen as its ionization threshold is at 15.58 eV; this is why it is crucial to determine if they can reach the reactor. As metastable atoms are embattled in the neon flow, their diffusion characteristic time τD has to be compared with their travel time τt between the end of the discharge and the reactor entrance.

In our experimental conditions, the depopulation is mainly done by radial diffusion to the discharge which means that the metastable atom density depends on the Bessel function of the first kind J0 [START_REF] Moisan | Physique des plasmas collisionnels (Application aux dcharges hautes frquences)[END_REF]:

𝑛(𝑟) = 𝑛 0 × 𝐽 0 ( 2.405×𝑟 𝑅 ) (3)
The inverse of the diffusion characteristic time is then

1 𝜏 D = 𝐷 𝛬 2
where Λ, the diffusion length, equals

𝑅 2.405
where R is the radius of the tube. The neon metastable diffusion coefficient is D = 170 cm²/s at 1 Torr and 300 K [START_REF] Dixon | Decay of the triplet p levels of neon[END_REF]. In our working conditions, (P = 1 mbar, T = 300K, R = 4mm), the diffusion time of the neon metastable atoms is 𝜏 𝐷 = 1.6×10 -4 s.

For a neon gas flow Q = 4sccm, the velocity is V = 1.3×10² cm/s and the travel time on this 5 cm length is τt = 4×10 -² s. As τt >> 𝜏 𝐷 , the neon metastable atoms are destroyed before arriving to the reactive zone.

We are now sure that the only energy input from our lamp are the VUV photons, making it fully compatible to the kind of experiments we intend to perform.

Discharge length.

In order to increase the VUV photon flux, one can increase the microwave power deliver to the discharge, but this will modify the discharge length, which could then enter the reactor. This explains why we measured the length of the discharge downstream the surfatron device as a function of pressure in different conditions of power (Figure 5). The length increases with the pressure. Above 1 mbar, it depends only on the microwave power with a maximum of 18 cm at a pressure of 1.7 mbar and a power of 80 W.

Then, for further use for photochemistry, we know where the surfatron must be positioned in order to have the maximum of VUV flux without any induced plasma reactions whatever the pressure and/or the power are.

Characterization of the VUV source

In order to fully characterize the source in the VUV range, the intensities of the two neon resonant lines (Table 1) are recorded in different conditions of pressure and power for the discharge.

Typical spectra recorded for the two resonance lines of neon are presented on Figure 6. We notice that the two lines present different behaviours regarding the pressure, this is why we will study them separately.

In order to calculate the VUV flux emitted by the surfatron source, we need the spectral responses of both the grating and the photodetector, without forgetting the absorption of the neon present inside the monochromator as described in section 1.2. The calculations have been performed first on the 73.6 nm line for different gas pressures and microwave powers (Figure 7; Figure 8). The order of magnitude of the source photon flux is 10 14 ph/s/cm², with a maximum of 4 × 10 14 ph/s/cm² (1.7 mbar and 100 W) and a minimum of 2 × 10 13 ph/s/cm² (0.4 mbar and 40 W). Figure 7 shows how the photon flux of the lamp varies versus the pressure for different values of power. It reveals a general profile of quadratic growth regarding the neon pressure as fitted on the orange curve on Figure 9.

On Figure 8, the variations of the photon flux versus the power delivered into the discharge are presented, for different values of pressures. Here, the growth looks linear.

These two trends versus the pressure and the power can be explained by a collisional radiative model. The radiative level is populated by electron collisions from the neon ground state and depopulated by line emission. The intensity of the 73.6 nm line is given by equation 4 where ne is the electron density,

[Ne] represents the neon concentration in its fundamental state, 𝜈 𝐿 is the inverse of the lifetime of the radiative level and k an excitation coefficient function of the electronic temperature:

𝐼(73.6 𝑛𝑚) ∝ 𝑛 𝑒 [𝑁𝑒]𝑘(𝑇 𝑒 ) 𝜈 𝐿 (4)
In our pressure range, we assume that the electron energy remains practically constant which means that the ionization degree is supposed to stay constant as well. For a given power, raising the gas pressure would then directly increase the neon density [Ne] but also the electron density ne which explains the quadratic law of the 73.6 nm line intensity. Moreover, at a fixed pressure, increasing the delivered power would here have a linear impact on the electron density ne, while the electronic temperature Te and the neon concentration remain constant.

We can now focus on the evolution of the 74.3 nm line.

When the 74.3 nm photon flux is plotted versus the pressure for an arbitrary power of 70 W, it looks like it does not follow the same quadratic trend as the 73.6 nm one (Figure 9). In fact, its intensity varies very linearly with the pressure which means that another phenomenon counterbalances the expected quadratic rise of the photon flux. In addition to the depopulation of this energy level by radiative photon emission, one lead is to involve a quenching effect. The lifetime of the radiative level 3 P1, that emits the 74.3 nm line, was measured by [START_REF] Phelps | Diffusion, de-excitation, and three-body collision coefficients for excited neon atoms[END_REF]) in parallel to the two metastable states 3 P2 and 3 P0 (Figure 10). These lifetimes are quite similar (few ms). As the 74.3 nm line is resonant, its level 3 P1 is re-populated and its density is on the same order of magnitude than the metastable states as [START_REF] Ricard | Production of Metastable and Resonant Atoms in Rare-Gas (He, Ne, Ar) Radio-Frequency and Microwave-Sustained Discharges[END_REF] has measured in a neon microwave discharge.

The quenching coefficient of the 3 P1 radiative level (at 16.67 eV) due to the transfer towards the 3 P2 metastable state, is ku = 4.2×10 -14 cm 3 /s [START_REF] Phelps | Diffusion, de-excitation, and three-body collision coefficients for excited neon atoms[END_REF]. The efficiency of this quenching is related to the small energy gap of 5.17×10 -2 eV between those two states. After collision, this energy is shared between the two atoms and corresponds to a temperature of approximately 300 K, which is more or less the gas temperature in the discharge.

Equation ( 5) gives the intensity of the 74.3 nm line taking into account this potential quenching effect.

In this equation, 𝜈 𝐿 corresponds to the inverse of the 3 P1 level lifetime. Then, the quenching seems to be dominant here, this is why the 74.3 nm line intensity increases linearly with the electron density and thus the pressure.

𝐼(74.3 𝑛𝑚) ∝ 𝑛 𝑒 [𝑁𝑒]𝑘(𝑇 𝑒 ) 𝜈 𝐿 + 𝑘 𝑄 [𝑁𝑒]
(5) For the 73.6 nm line, which corresponds to the 1 P1 level, the quenching is less efficient, because the transfer to the 3 P0 metastable state presents a higher energy gap of 0.133 eV i.e a temperature of 770 K for each atom, too hot for our experimental conditions. This level is then mainly depopulated by radiative transfer.

To conclude, the pressure at which we are working will determine which line(s) will contribute to our photochemistry experiment. For high pressures (P > 0.7 mbar), the radiative emission from the 73.6 nm line is clearly dominant compared to the steady contribution of the 74.3 nm one. However, when going low in pressure the contribution of both lines have to be taken into account.

First photochemistry experiment

When the source is coupled to the APSIS reactor, an N2-CH4 mixture (95% N2, 5% CH4) is injected. First, 4 sccm of neon are injected inside the discharge tube, which corresponds to a discharge pressure P = 1.3 mbar. In a second time, in order not to contaminate the discharge, we inject 2 sccm of N2-CH4 in APSIS for a pressure of 0.9 mbar. This neon flow permits a relevant photon flux for the VUV source but also prevent the reactive N2-CH4 mixture from entering the discharge tube, this is why we chose it for our first photochemistry experiment. The power delivered to the discharge is Pw = 80 W which corresponds to a photon flux of 1.9×10 14 ph/s/cm² or 0.95×10 14 ph/s for the tube section of 0.5 cm².

Two effects have to be monitored by mass spectrometry: first, if the reactive signals are getting lower through the experiment, as it would mean that there is an effective consumption due to the photon interaction; and, in a second time, the signals of some hydrocarbon and/or N-bearing species (Titan-like molecules) are followed in the expectation of seeing a production. Here, we focus on the mass m/z = 15 in order to represent the CH4 reactive, through its CH3 + fragment, because the real CH4 mass m/z = 16 can overlap multiple species fragments. In addition, we look at some Titan-like molecules: m/z = 27 for The presence of those molecules highlights the incorporation of both C and N atoms coming from the expected dissociation of N2 and CH4. Methane has been identified as a key reactant to initiate efficient organic growth, in contrast to the other major form of carbon commonly found in planetary atmospheres, carbon dioxide CO2. However, methane chemistry leads to the only production of complex hydrocarbon molecules, with no heavy heteroatoms of interest for prebiotic chemistry such as nitrogen [START_REF] Raulin | Prebiotic-like chemistry on Titan[END_REF]. N2 photolysis leads to reactive forms of nitrogen, atomic or ionized, which react with hydrocarbons to produce nitrogen containing organic compounds. These nitrogen containing species have a strong interest for prebiotic chemistry [START_REF] Dutuit | Critical review of N, N +, N + 2, N ++, and N++ 2 main production processes and reactions of relevance to Titan's atmosphere[END_REF]. The most abundant gas-phase nitrogenbearing products in Titan atmosphere are nitriles molecules (R-CN) as the HCN and C2N2 molecules that we found in our experiment. The goal of the photochemistry experiment is then achieved, which ends to validate the suitability of the VUV source.

DISCUSSION

For our atmospheric applications, we compare those data to the solar flux. As a matter of fact, at Titan the solar flux is of 10 7 ph/s/cm² at 75 nm. This means that our N2-CH4 reactive medium receives approximately 10 7 more 75 nm photons making the chemical reactions more efficient in terms of kinetics.

It is interesting to compare the photon flux numbers to the ones of the VUV DESIRS beamline at the synchrotron SOLEIL (France) which offers a wide energy range between 5 and 40 eV (or 31 to 248 nm). At approximately 17 eV (~75 nm) and for a resolving power of 1000, between 7×10 12 ph/s/cm² for a 4 mm × 8 mm spot and 10 16 ph/s/cm² for a 200 µm×100 µm spot are delivered [START_REF] Nahon | DESIRS: A state-of-the-art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL[END_REF].

Despite providing only one specific wavelength at a time, our source is then competitive to a VUV synchrotron beamline regarding the photon flux as it goes from 2 × 10 13 ph/s/cm² up to 4 × 10 14 ph/s/cm².

Regarding the pressures, the one in the photochemical reactor is higher than in Titan's upper atmosphere but this prevents any undesired wall effect [START_REF] Carrasco | VUV photochemistry simulation of planetary upper atmosphere using synchrotron radiation[END_REF]. Moreover, our setup does not requires a differential pumping system between the source and the 1 mbar reactor; which is unavoidable at a synchrotron beamline where the source is under ultra-high vacuum at 10 -8 mbar.

Conclusion

So, in conclusion, VUV plasma source based on surfatron-driven microwave discharges have proven to be an efficient and reliable tool for VUV atmospheric photochemistry experiments working at low pressure. For the ones using neon, it has been demonstrated here that the only energy source injected inside the reactive medium is the VUV photons from its two resonant lines (73.6 and 74.3 nm). Other sources are indeed possible (neon metastable atoms and electrons from the discharge) but the system has been adapted so that they will not disturb the desired pure photochemistry. In this case, the key parameter appears to be the distance between the end of the discharge and the entrance of the photochemical reactor. Also, always for neon, the behaviours of the two resonant wavelengths have been investigated in order to characterize their contribution in several conditions of pressure and power. The 73.6 nm line is largely dominant in our working conditions, but its intensity decreases with the pressure (quadratic law) and the power (linear law). This behaviour is different from the 74.3 nm line which remains quite stable whatever the pressure or the power are, possibly because of a quenching effect. It results that at low pressure (P < 0.7 mbar) the 74.3 nm one becomes dominant. To further investigate these relative intensities, a complete modelling of the discharge in our conditions taking into account the electron energy distribution function would be required. In fact, according to [START_REF] Zissis | Influence du mode d'alimentation sur la production du rayonnement VUV des raies de résonance de Ne dans une décharge électrique à basse pression[END_REF] and their model with a 10 Torr DC discharge, the 74.3 nm line has a higher intensity than the 73.6 nm one, which is not in agreement with our experimental results.

Moreover, at 73.6 nm, the order of magnitude for the photon flux is 10 14 ph/s/cm², which seems largely comparable to a VUV synchrotron beamline at specific wavelength. The working conditions of the surfatron-based VUV source are quite flexible (regarding the pressures and power), allowing the photon flux to vary from 2 × 10 13 ph/s/cm² up to 4 × 10 14 ph/s/cm² and offer measurable photochemistry results.

Our new setup, without any window separating the source and the photoreactor, can change the way atmospheric photochemistry experiments have been performed so far, especially for the ones focusing of nitrogen-dominated atmospheres such as the Earth, the Early Earth, Titan or Pluto.

More specifically, our setup showed its ability to simulate the formation of nitriles in Titan's atmosphere. Those are not correctly predicted by the current photochemical models [START_REF] Loison | The neutral photochemistry of nitriles, amines and imines in the atmosphere of Titan[END_REF].

Even the simplest and most abundant nitrile, HCN, is found to be predicted by neutral photochemistry with concentrations three to ten times larger than measured by the Cassini space mission [START_REF] Hébrard | Neutral production of hydrogen isocyanide (HNC) and hydrogen cyanide (HCN) in Titan's upper atmosphere[END_REF]. Such disagreements between model predictions and observations reveal a poor knowledge of the chemistry involving nitrile in general and HCN in particular. Without the constraint of adapting the system to high pressure gradients between the source and the reactor or the low availability of synchrotron beamlines, our experiment will provide the opportunity to explore the chemistry of nitriles and improve our knowledge in this area.

Acknowledgments.

S. Tigrine would like to thank the IDEX Paris Saclay for her Phd thesis grant and N. Carrasco thanks the ERC Starting Grant PRIMCHEM, grant agreement n°636829. The Centre National d'Etudes Spatiales (CNES) supported the design of the APSIS reactor. The characterization of the VUV source has been possible thanks to the monochromator available at the Plateforme d'Integration et de Tests (PIT) at the Observatoire de Versailles Saint Quentin (OVSQ). All the authors also wish to thank Dr L. Nahon for his kind support and advices.

Ádámkovics, M., 2003. Photochemical formation rates of organic aerosols through time-resolved in situ

Figure 1 :

 1 Figure 1: VUV absorption cross sections of N2 (blue) and CH4 (green), and the VUV solar spectrum at Titan (red). The dotted vertical lines show the VUV emission lines of the three rare gases He I, Ne I, Ar I.

Figure 2 .

 2 Figure 2. Scheme of the photochemical reactor coupled windowless with the VUV source.

Figure 3 .

 3 Figure 3. Typical UV spectrum of the neon discharge (black curve). Only Ne I lines listed in the NIST data base are observed. The red curve shows the same UV spectrum when plasma reaches the entrance of the reactor and the N2 SPS bands are visible (Lofthus & Krupenie 1977).

Figure 4 .

 4 Figure 4. UV spectrum with neon in the discharge tube (blue) and neon facing APSIS filled with the N2-CH4 mixture (orange). The fact that the two spectra are exactly the same shows that N2 is not excited by the discharge.

Figure 5 :

 5 Figure 5: Length of the neon microwave discharge (downstream the surfatron device) for different conditions of pressure and power.

Figure 6 .

 6 Figure 6. The two resonant emission lines of Ne I at 73.6 and 74.3 nm at 70 W for two different pressures showing different intensity ratio between the two lines.

Figure 7 .

 7 Figure 7. Photon flux emitted by the neon microwave discharge in different conditions of power versus the pressure. At high powers (Pw >70 W) and high pressures (P >1.5 mbar), the amplifier saturates this is why the data are not shown on this graph.

Figure 8 .

 8 Figure 8. Photon flux emitted by the neon microwave discharge in different conditions of pressure versus the power.

Figure 9 .

 9 Figure 9. Compared photon flux evolution, in function of the pressure, of the two neon emission lines at 73.6 and 74.3 nm for an arbitrary given power of 70 W and their quadratic and linear fits (respectively).

Figure 10 .

 10 Figure 10. Gotrian diagram of the neon energy levels taken from[START_REF] Phelps | Diffusion, de-excitation, and three-body collision coefficients for excited neon atoms[END_REF]

Figure 11 .

 11 Figure 11. Time-monitoring mass spectrum in MID mode following the consumption of the reactive CH4 (top) and the production of the HCN and C2N2 molecules (bottom). The red dotted lines mark the beginning of the irradiation of the APSIS reactor with the VUV source.

Table 1 .

 1 Resonance lines of He I, Ne I and Ar I (NIST database).

	Gas	Wavelength (nm)	Aki (s -1 )
	He I	58.43; 53.70	1.8 × 10 9 ; 5.66 × 10 8
	Ne I	73.59 ; 74.37	6.11 × 10 8 ; 4.76 × 10 7
	Ar I	104.8 ; 106.66	5.1 × 10 8 ; 1.19 × 10 8